cura me poto – lim pa uno how i poto ™ me poto - lim pa uno how i poto - buk me... · dok cen i...

Functional Numeracy for Food Security and

Nutrition

Cura me poto – Lim pa Uno How i

poto ™ Buk me 3

Byeka me cek pa gin apura ki rwom me dit

pa dero cam ma mite.

Cura man kub lim me 9-12 i poto

Cura me poto – Lim pa Uno How i poto ™

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Functional Numeracy for Food Security and

Nutrition

Cura me poto – Lim pa Uno How i

poto ™ Buk me 3

Lim me 9-12 i poto

Byeka me cek pa gin apura ki rwom me dit

pa dero cam ma mite.

William Ian Robinson Lisa Osborne (Graphics)

Heather Pitcher

April 2016


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Lim pa Uno How i poto ocung ikom kwano

diro me cura ma time ki i oot pa lanywak tam ki

lopur ma kilwonge ni “Uno How”. Lim ki pwonye

man lubo lawote kore ki kore.

Nyutu program

Buk me 3 - Byeka me cek pa gin apura ki rwom me dit pa dero cam ma mite.

Buk man mede ki ikom lim me 8 pa “Uno How” i poto, man mede ki iwi buk me 1 ki 2 (ki miyo pir gi ma cego cego piny eno. Buk magi bene tye ma komgi ki acel acel). Lim me 9 – Byeko wel tunu anyogi ducu ma tye i poto Lim me 10 – Byeko wel cam ma tye I dero cam/citua Lim me 11 – Byeko dit pa gin apura ma nyige ma tye I poto Lim me 12 – Byeko dit pa dero cam/citua ma mite – lapo wic/kwan odoco

Lim magi ki nyutu pire ki cal agoya mogo me yabu wii pwonye ducu. Topik acel acel dong lube ki lok atita, labol, ki dong tic atiya lubu kore.

Buk me 1 - Cura me nongo dit pa poto Lim me 1 - Pimo poto ma meri Lim me 2 - Timo cura me nongo dit pa poto ma meri Lim me 3 - Timo cura me nongo dit pa poti ma orwange Lim me 4 - Byeko dit pa poto ma kamegi

Buk me 2 - Byeka me dit pa kodi, Fetalaiza ka dong yat akira ma mite Lim me 5 – Dwong pa kodi ma mite Lim me 6 – Wel cente ma mite pi Kodi Lim me 7 – Byeko dwong pa fataliza ma mite Lim me 8 – Dwong pa yat akira ma mite Buk me 1, 2 ki 3 twero nonge dok kwanye ki i: http://www.agritechtalk.org/Uno How Introduction.html

http://www.agritechtalk.org/Uno%20How%20Introduction.html


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Lim pa Uno How i poto

Pot karatac ma nyutu jami ma I buk man

Lim pa Uno How me 9 i poto… – Byeko wel tunu anyogi ducu ma tye i poto .......................... 4

Purudakcon/pur ki kac. ................................................................................................................ 5

Yero dwong ki ka bedo pa lanyut ipoto ........................................................................................ 6

Tic ki latwoke angwen me nongo lanyut pa cam ma tye kadongo ii m2 1 ..................................... 8

Kwano tunu anyogi ki cam ma tye kadongo ............................................................................... 11

Cura me nongo wel katikati pa cam ma tye kadongo i m2 acel acel ........................................... 12

Timo cura me nongo katikati pa wel tunu anyogi ma tye kadongo pi tyen anyogi acel acel. ...... 14

Cura me nongo katikati pa wel tunu anyogi ma tye ii m2 1. ........................................................ 16

Byeko wel tunu anyogi ducu ma tye i poto ................................................................................. 17

Lim pa Uno How me 10 i poto…Byeko wel cam ma tye ii citua nyo dero cam ....................... 20

Pimo dit pa dero ma kit gi padi padi. .......................................................................................... 21

Pimo dwonge pa cam ma pe ki dino ma tye i citua. ................................................................... 29

Byeko wel tunu anyogi nyo wiye i dwonge ma ki miyo. .............................................................. 31

Byeko wel tunu anyogi ducu ma tye ii citua. .............................................................................. 33

Pimo pek lanyut me cam. .......................................................................................................... 34

Tic ki pek pa lanyut me byeko pek pa cam ducu ma tye i dero. ................................................. 35

Tic ki pek me byeko pek pa cam ma tye i dero. ......................................................................... 36

Lim pa Uno How me 11… Byeko cek pa nyig cam ma pud tye i poto. .................................... 38

Pek pa cam (wel cam ma tye kadongo). .................................................................................... 39

Kwano tunu anyogi ki cam ma tye kadongo (Kwan odoco/Lapoo wiic). ..................................... 40

Byeko well tunu anyogi ma tye i m2 1 (Lapoo wiic). ................................................................... 41

Byeko pek nyo pa nyig cam ma oaa ki i tunu anyogi nyo wii cam acel. ...................................... 43

Byek pek pa nyig kodi ma okati ki ii m2 1 ma pur otime iye. ....................................................... 45

Byeko pek pa nyig kodi ma tye i poto. ....................................................................................... 46

Byeko pek pa nyig cam ma tye ipoto matino, dok nongo poto man pe tye ma rom – gin akwana

ma ki medo. ............................................................................................................................... 47

Lim pa Uno How 12 i poto… Byeko dit pa dero cam/citua ma mite – lapo wic/kwan odoco . 48

Cura me nongo dwonge pa cailo (lapo wic/kwan odoco). .......................................................... 49

Cura me nongo rwom me gwoko cam pa dero/citua. ................................................................. 50

Pimo dwonge pa oduu (Kwan adoco). ....................................................................................... 51

Byeko pek pa nyig cam ma tye i oduu. ...................................................................................... 53

Wel kicaa ma mite. .................................................................................................................... 54

Lagam pi Lapeny me atima pi Cawa Manok .............................................................................. 56


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Lim pa Uno How me 9 i poto…Byeko wel tunu anyogi ducu

ma tye i poto

Liim pa Uno How me 9 ii poto otum – Mede ii liim me 10 pa Uno How ii poto


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Ngeno wel tunu anyogi ma gitye kwede i poto ma megi konyo Tad ki Mim me:

Neno tunu anyogi adii ma gin twero cato madyak, Kun kadi kabed kumeno, gin pud bedo

ki kero me neno ni gin pud kitye ki anyogi me atwoya ki atinya ma oromo pi acata nyo

acama lacen.

Goyo pulan /gin atima me dit pa dero cam ma mite pi gwoko cam ma megi iyoo nge

kaac.

Lim pa Uno How me 9 i poto

Byeko wel tunu anyogi ma tye i poto

Purudakcon/pur ki kac.

Purudakcon/pur ki kac obedo wel cam ducu ma ocek. Pol kare ki nyutu ki pek pa nyig kodi (labole Kg/lapim nyo MT) nyo bene ma calo dit pa wel dul kom gin apura ma cate (Labole, wel tunu anyogi ma okati) Kaac obedo wel cam ma okati ki i pur ma otime ki ngom ma rwom me dite ki ngeyo. Pol kare ki Waco pire i kg nyo tan (MT) pi hecta acel acel. Man bene twero nyute ki neno wel gin ma cate ma okati ki ipoto, labole- wel tunu anyogi ducu ma okati ki i hecta acel acel. Tad ka Mim tye ka timo cura me nongo kit ma anyogi gi ocek kwede kun gitiyo ki wel tunu anyogi ma okati ki i poto ma megi.

Yoo ma ber loyo ducu me neno wel tunu anyogi adii ma ocek en aye me kwano tunu pa anyogi ducu ma okati ikare ma itye ka turu gi ki ipoto, ento man mito cawa madwong tutwal. Anyogi pa Tad ki Mim pud dong tye ipoto. Kimeno, gin myero obyek kaac ma megi ki kwanyo lanyut pa cam ma tye kadongo ipoto ma megi. Kwanyo lanyut kakany tere aye niya:

Kwano tunu anyogi i kabedo ma pol idye poto kun nongo ineno ni ariya man dit ma megi rom aroma (m2 1), macalo kit ma Tad ki Mim tye katimo neni.

Tic ki wel katikati pa tunu anyogi ma tye ikabedo ma lanyut ki kwanyo ki iye me byeko wel tunu ducu ma tye ipoto Kit ma dit pa kabedo ma lanyut/lanyut kikwanyo ki iye pol kare tye cikweya mita acel ni:

o Nyayo wel katikati me tunu anyogi ma tye ii cikweya mita 1 ki 10,000 bino miyo byek me wel tunu anyogi ducu ma tye i hecta acel. (wi opoo niya, m2 10,000 = hecta 1)

Dok cen i lima pa Uno How me 9 i poto

Tad ka Mim mito ngeyo wel tunu anyogi adii ma gin opuru ki ipoto ma megi wek okony gi me neno

kit ma cam gi ocek kwede.


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Tam ka Mim mite ni myero gukwany lanyut pa cam gi ma tye ipoto wek gin onge tunu anyogi adii ma tye ipoto ma megi. Wek man otime, myero gin obyek anyogi adii ma tye kadongo ii m2 1, ki bene tunu adii ma tye ii tyen anyogi acel. Nyayo wel magi ducu kacel miyo byeka me wel tunu anyogi ma tye ii m2 acel. Wel tunu anyogi ducu ma tye ii poto twero byeke ki nyayo wel tunu anyogi ma tye ii m2 acel I dit pa poto ducu (ii m2). Me byeko wel tunu ducu ma okati ki i hecta acel, wel tunu anyogi ma okati ki m2 acel ki

nyayo ki 10,000

Nongo wel pa kabedo me lanyut

Wel kabedo cung ikom dit pa poto. Pi byeka ma ber, lanyut madwong pore pi poti madongo ento pe pi poti ma tino tino.

Pi kwed me oyot oyot, ka ma nongo repot mite ikin kare ma nok, myero inen ka poto ma megi tye marom (dongo pa cam tye ma rom ikabedo ducu me poto enoni) nyo apoka poka tye (cam pe tye kadongo marom ipoto men)ka dong myero ki yer cac-ce nyo wel kabedo ma rwate.



Yero dwong ki ka bedo pa lanyut ipoto

Me nongo byeka ma ber loyo, pire tek ni lanyut myero ocung pi poto ducu. Man tere ni, ka bedo pa lanyut (tecen) myero ki kwany marom pi pot dok nongo cung pi poto ducu liweng. Kabedo pa lanyut twero moke ki:

Poko poto marom ki wang, ma myero obed idul ma ki coyo coc nyo namba/wel ma cung pi

kabedo acel acel. Yero wel magi lobongo neno ne (tere ni, ki kwanyo ataa) me moko

kabedo ma lanyut myero okati ki iye. Me nongo kom ka kwene kikome ma lanyut myero

oaa ki iye, tal ma cek ma ki coyo wiye tung cel ki twero bayo ne “lamiya wang” ii kabedo

moni ka dong lanyut ki kwanyo…kun nongo tal ma cek ma tere ki coyo ni nongo tye icwiny

dye m2 aceli.

Malube ki yoo me kwanyo lanyut ma dong kimoko pire mapud peya kidonyo ipoto ni, yoo

eno ni kilwongo ni “trancek” ma aye: yoo ma neno ki coyo rekod obino time pi konyo moka

mukene me anyim. Kabedo pa lanyut myero obed marom aroma ki dong pe dok ma bor

tutwal

Tad ki Mim tye ka byeko cek pa cam me megi kun gi

tiyo ki wel tunu anyogi ma tye ipoto ma megi. Gin

guwoto i nukta – W ipoto ma megi, gi cung ikabedo ma

pat pat me kwanyo lanyut, man kilwongo kabedo. Wi

opo ni kit me kwanyo lanyut ki nyutu pire wiye wiye ii

Buk me 2 - Lim me 8.


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Poto marom Poto ma pe rom

Wel kabedo me lanyut ki kabedo gi kicoyo imeja ma tye piny ni kun lubu caji/dit pa

poto ka dong ka cam tye ka dongo marom nyo ma pe rom

Dit pa poto

Poto marom Poto ma pe rom

0 - ha 0.5 (nucu eka)

Kabedo1 ki kwanyo ataa icwiny dye poto, ki gucu tal macek/ lagweng angec angec kun nongo kato ki iwi gwook.

Kabedo 2 (nyo ikare mukene 3) : kabedo acel ki yero mere ataa (taal ma cek ma ki coyo tere ki bolo kun dok angec angec kun kato ki iwi gwok) kun dok ii “zon” (kabedo) acel acel ka ma cam nen tye kadongo ma rom rom.

0.5 - ha 2 Kabedo 3: Lobongo yero ayera (kwanyo lamiya wang) wot kun ilworo poto nyo i wot i trancek ma i donyo iye ma tye atir kun nongo woto aryec kun ngolo dye poto arii ( man pe myero olub lak poto)

Kabedo 5: Nukta– W myero ki wot iye kun nongo ngolo dye poto arii; man myero obed ma nongo lac kin gi nongo tye marom aroma.

2 - ha 5 Kabedo 10: Nukta – W myero ki wot kun nongo bene ngolo dye poto arii. NB: Med lac kin acel acel ma lubu kit ma dit pa poto tye ka mede kwede – ento lac kin gi magi myero obed rom aroma ikin kabedo ducu.

Kabedo 10: tracek ma tye nukta – W myero ongol dye poto ducu. Nen maber: Med lac kin kabedo acel acel ma lubu kit ma dit pa poto tye ka mede kwede.

5 - ha 10 Makato kabedo 10: trancek ma tye nukta – W (man cung ikom cawa matye)

Makato kabedo 10: trancek ma tye nukta – W (man cung ikom cawa matye)

Meja ma piny eno ni miyo ngec ikom kit me yero wel lanyut ki kabedo ma pi kit poti ma padi padi:

Poto pa Tad ki Mim tye ma pe rom pime tye ni ha.1.23. Kit ma meja ma maloni nyutu, gin myero okwany lanyut ki ii kabedo 5 ma padi padi (lanyut me acel ni oo I lanyut me abic) ii nukta – W kun nongo ngolo dye poto alutu. Dok cen i lima pa Uno How me 9 i poto

S1 S3

S2

S5

S4


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Kit ma latwoke angwen kitiyo kwede kede cung ikom boco pa cam ma tye kadongo ipoto. Pi cam ma dongo ma boco, labole anyogi, latwoke angwen ki tiyo kwede ma nongo ki yabu cinge ariyo.

Mak bad latwoke angwen aryo kun nongo iyabo ii angul cingi ma lacuc (man angul 900), man myero iket I agiki me wang pyer.

Rye cing latwoke angwen wek owoti ikom cam ma ocung nyo tye kadongo.

Tii keken ki cam ma tye kadongo matye i ariya ma bad latwoke angwen oo iye ni keken ma calo lanyut ma megi.

Kwan ka i coo piny well tyen anyogi nyo cam ma tye kadongo ka bene tunu anyogi ma tye i m2 acel acel.

Pi cam mogo ma dongo macego, cing latwoke angwen angwen ducu ki tiyo kwede:

Yab latwoke angwen wek oyub cikweya.

Ket latwoke angwen iwii ngom.

Tii keken ki cam ma tye kadongo ma tye i latwoke angwen I lanyut ma ka megi.

Kwan ka i coo piny wel tyen cam ma tye kadongo ki bene dul kom cam eno ni ma rwom me acata ne tye. Man ducu myero otime keken i m2 acel acel.

NB: Pire tek tutwal ni cam ma tye kadongo ma okati woko ki i ngom matye i latwoke angwen keken aye ma kitiyo kwede.

Ka itye ka kwanyo lanyut, Uno How tye ki latwoke angwen, latwoke angwen ma yot dok kobe pi oyot oyot. Latwoke angwen ma man tye ki ariya me iye ma tye m2 1.

Uno tiyo ki latwoke angwen ma kiyubu ki nyonyo ma tye ki mwot itwoke ducu. Man konyo weko twero dole dok pike I jeba k ace tice pud pe nyo dong otum.

Latwoke angwen kitwero tic kwedgi macalo cikweya, ma nongo cingi angwen weng kikubo nyo bene manongo cinge ariyo keken ki yabo.

Ka pe itwero nongo latwoke angwen, you ma yot dok cek en aye me ngolo lut ma beco ariyo

nyo angwen (lut man myero obed tego ma gin ducu bor gi myero obed m 1 kadong imak gi ii

cingi kun nongo yubu gul cingi ma lacuc.



Tic ki latwoke angwen me nongo lanyut pa cam ma tye kadongo ii m2 1.


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Latwoke angwen ma bade ariyo kiyabo. Latwoke angwen ma bade angwen duc kiyabo.

Wii opo niya: lanyut kikwanyo ki ikabedo angwen pi acel acel.

Kwany lanyut me acel ka dok inwo tic enoni tyen adek mukene (tyen 4 ducu). Lok 900 iyo nge

kwanyo lanyut acel acel, wot kacel ki latwoke angwen, kun nongo igwoko tyeni i kabedo ma

idyere ni. Man ki nyutu pire piny eno:

Wir 900 me dok tung acuc (kit ma cing cawa woto kwede) tyen 3, man me weko m2 1 ki kwany

lanyut iye tyen 4 i acel acel.

.


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Pi cam mogo ma tyengi pe calo tyen anyogi (labole, kal), tii ki twok latwoke angwen angwen ma

tye iwii ngom, kun nongo ibano iwii lawote wek owum cikweya 4 ma tye oromu dyere ka ma en

tye ka wire ki iye ni.

Lapeny me atima pi cawa manok 1- Kati ki wel kabedo me kwanyo lanyut.

Co lagam ma megi piny ka dong inen gi ka tye kakare ki iyi agiki me buk man.


1. Lapur tye ki poto ma pe rom ma dite tye ha 1.5. Pulan me poto man kinyutu pire piny. Lanyut adii ma lapur man myero okwany ki dong ki ka kwene pa poto man?

2. Lapur tye ki poto ma dite tye ha 0.75. Poto man tye ki cam ma rom aroma. Lanyut adii ma lapur man myero okwany ki dong myero okwany ki ka kwene pa poto man?

3. Lapur tye ki poto madite tye eka 6 (ha 2.43). Cam ma tye ipoto man tye marom aroma. Ki ka kwene ma lapur man myero okwany lanyut ki iye ki dong lanyut adii ma myero en okwany? Ki dong kono ka onongo cam ma mege pe tye ma rom aroma?


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Citep man medo ki byeko wel tunu anyogi ma tye ipoto, kun nongo itiyo ki wel lanyut ma in icoyo piny. Citep me 1: tii cura me nongo wel katikati pa cam ma tye kadongo i m2 1 (wel cam ma tye kadongo) pi lanyut duc ma megi.

Citep me 2: Tim cura me nongo wel katikati me tunu anyogi pi tyen anyogi acel acel pi lanyut ma kamegi.

Citep me 3: Nyaa adwogi me citep me 1 ki citep me 2 me nongo katikati me tunu anyogi/m2 pi lanyut

Citep me 4: Nyaa adwogi me citep me 3 ki ariya me dit pa poto (i m2) me byeko wel tunu anyogi ducu ma tye ipoto. Citep magi kitito pire kore ki kore ipot karatac ma olubu man. Me weko onen ni itimo man iyoo ma opore, pire tek ni igwok rekod maleng ki dong adwogi pa cura ni maber. Meja ma calo tye piny eni, kun nongo tye ki rek acel acel, twero konyi wek itim man:

Tecen Lanyut me 1 (m2 1) Lanyut me 2 (m2 1) Lanyut me 3 (m2 1) Lanyut me 4 (m2 1) Wel cam ma

tye ka dongo (tyen anyogi)

Wel tunu anyogi

Wel cam ma tye ka dongo (tyen anyogi)

Wel tunu anyogi


Wel tunu anyogi


Wel tunu anyogi

T1 T2 T3



Kwano tunu anyogi ki cam ma tye kadongo

Uno, Tad ka Mim okwanyo lanyut ki ipoto ma dite tye ha 1.23. gin gutiyo ki 5 (T1-T5), kun nongo tye ki lanyut 4 pi kabedo acel acel weko wel lanyut ducu bedo 20. Pi lanyut acel acel, gin gicoyo wel tyen anyogi ki wel tunu anyogi piny. Adwogi ne tye kit ma kinyutu pire imeja ma tye piny eno:

Tecen Lanyut me 1 (m2 1) Lanyut me 2 (m2 1) Lanyut me 3 (m2 1) Lanyut me 4 (m2 1) Wel cam ma

tye ka dongo (tyen anyogi)

Wel tunu anyogi


Wel tunu anyogi


Wel tunu anyogi


Wel tunu anyogi

T1 4 6 3 5 4 4 5 5

T2 5 5 6 7 0 Cam ma tye kadongo pe

5 4

T3 5 6 4 5 3 4 0 Cam ma tye kadongo pe

T4 2 3 6 5 5 5 3 3

T5 7 6 4 6 4 3 5 5


Me byeko wel tunu anyogi ma tye i poto, tunu

anyogi kacel ki tyen anyogi ma tye kadongo ki

kwano gi pi lanyut acel acel.


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Citep me 1: Tim cura me nongo katikati me wel cam ma tye kadongo i m2 acel acel Tad ka Mim gumedo wel tyen anyogi ducu ma oaa ki I lanyut 4 ma kikwanyo ki i acel acel. Kombedi gimito nongo wel katikati pa cm ma tye kadongo i lanyut me m2 1 ka ma acel acel tye iye, kadong gipoko ki 4. Katikati me wel cam ma tye kadongo/m

2 pi acel acel =

wel cam ducu ma tye kadongo ma tye i acel acel

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Cura me nongo wel katikati pa cam ma tye kadongo i m2 acel acel

Adwogi kor tic kinyutu pire piny eno ma calo labol:

Tecen Wel cam ma tye ka dongo (tyen anyogi)

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Wel cam ma tye kadongo ducu

Katikati me wel cam ma tye kadongo/m2

T1 4 3 4 5 16 4

T2 5 6 0 5 16 4

T3 5 4 3 0 12 3

T4 2 6 5 3 16 4

T5 7 4 4 5 20 5

Tic ki katikati man, dong kombedi gin twero nongo katikati ducu ki pete tere. katikati ducu ki pete tere pa cam ma tye ka dongo i m2 acel acel =

katikati duc ma ki toro pa cam ma tye kadongo/m2 pi acel acel Wel ducu

Tad ka Mim medo katikati me acel acel kadong gi poko ki wel ducu, ma en aye 5: 4 + 4 + 3 + 4 + 5 = 20 / 5 = 4 Cidong, katikati pa wel cam ma tye ka dongo pi m2 acel acel tye 4.


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Lapeny me atima pi cawa ma nok 2 – Cura me nongo wel katikati pa wel cam ma tye kadongo ii cikweya mita acel



1 A farmer has 5 stations S1 to S5 with the following four plant counts per sq metre. What is the

overall average number of plants per sq m?

1 Lapur tye ki 5, T1-T5, lanyut acel acel tye ki cam ma tye ka dongo 4. Katikati pa cam ma tye kadongo ducu ki pete tere ducu dong tye adii / m2?


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Katikati me wel cam ma tye kadongo/m

2

T1 5 3 4 2

T2 4 7 4 1

T3 0 0 0 1

T4 2 3 3 0

T5 3 2 1 6

2 Katikati ducu ki pete tere pa cam ma tye kadongo /m2 dong tye adii ka lapur ocoyo piny adwogi me kwan magi pi 5 (T1-T5)?


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



2

T1 8 7 5 4

T2 7 6 4 3

T3 7 5 8 8

T4 0 4 6 7

T5 3 4 8 5

3 Kun itiyo ki adwogi pa kwan ma tye piny eni, tim cura me nongo katikati ducu ki pete tere pa cam ma tye ka dongo/m2.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



2

T1 4 5 0 1

T2 4 6 1 1

T3 2 4 6 0

4 Kun itiyo ki adwogi pa kwan ma tye piny eni, tim cura me nongo katikati ducu ki pete tere pa cam ma tye ka dongo/m2.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



2

T1 3 2 1 0

T2 4 3 0 1

T3 5 0 1 2

T4 4 2 2 2

T5 2 3 1 4


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Citep me 2: Tim cura me nongo katikati pa wel tunu anyogi ma tye kadongo pi tyen anyogi acel acel. Pi acel acel, Tad ka Mim otyeko medo wel tunu anyogi ducu ma oaa ki i lanyut 4 ma megi. Kombedi dong mite ni myero gin dong gunong katikati pa wel tunu anyogi ma tye ityen anyogi acel acel. Wel katikati pa wel tunu anyogi ma tye i tyen anyogi acel acel pi kabedo acel =

Wel tunu anyogi ducu ma tye i meno Wel tyen anyogi ducu ma tye i meno



Timo cura me nongo katikati pa wel tunu anyogi ma tye kadongo pi tyen anyogi acel acel.

Adwogi pa kor tic man kinyutu pire piny eno me labol.

Tecen Wel tunu anyogi

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Wel tunu anyogi ducu ma tye i

Wel tyen anyogi ducu ma tye i

Katikati me wel tunu anyogi ma tye ikom tyen anyogi acel acel.

T1 6 5 4 5 20 16 1.25

T2 5 7 Cam ma tye kadongo pe

4 16 16 1

T3 6 5 4 Cam ma tye kadongo pe

15 12 1.25

T4 3 5 5 3 16 16 1

T5 6 6 3 5 20 20 1

Tic ki katikati man, gin dong kombedi twero nongo katikati pi kabedo ducu. Katikati pa wel tunu anyogi pi tyen anyogi acel acel =

Katikati ducu ma kitoro pi tunu anyogi ma tye pi tyen anyogi acel acel Wel ducu

Tad ka Mim medo katikati me acel acel kadong gi poko ki wel ducu, ma en aye 5: 1.25 + 1 + 1.25 + 1 + 1 = 5.5 / 5 = 1.1 Kit meno, katikati me wel tunu anyogi pi tyen anyogi acel acel tye 1:1. Man obedo byeka me katikati pa wel tunu anyogi ma tye ityen anyogi acel acel pi poto kulu.


15

Lapeny me atima pi cawa manok 3 – Cura nongo katikati pa wel tunu anyogi ma tye pi tyen anyogi acel acel.



1 Lapur tye ki 5, T1-T5 ki wel tunu anyogi magi inge kwano ne pi lanyut acel acel ka dong welt yen anyogi ducu ma tye i meno. Dong katikati me wel tunu anyogi ducu ki pete tere adii ma tye pi tyen anyogi acel acel?


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



Katikati me wel tunu anyogi pi tyen anyogi acel acel pi acel acel.


Cam ma tye kadongo pe

5

T2 5 Cam ma tye kadongo pe

1 1 4

T3 2 1 3 2 2

T4 Cam ma tye kadongo pe

2 1 2 6


2 1 4

2 Lapur ocoyo piny adwogi me kwan magi pi 5 (T1-T5). Dong katikati ducu ki pete tere pa wel tunu anyogi pi tyen anyogi acel acel tye adii?


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4





1 4

T2 1 2 3 1 6


3 Cam ma tye kadongo pe

1 5


7

T5 3 1 1 2 8

3 Katikati ducu ki pete tere pa wel tunu anyogi pi tyen anyogi acel acel k ace lapur ocoyo piny adwogi magi pi 3 (T1-T3)


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4




T1 4 4 1 5 7

T2 4 5 2 1 5

T3 2 3 1 2 5


16

Citep me 3: Cura me nongo katikati pa tunu anyogi ma tye i cikweya mita acel acel (tunu

anyogi/m2)

Katikati me wel tunu anyogi/m2 = Katikati me wel tyen anyogi/m

2 x Katikati me wel tunu anyogi ma

tye i tyen anyogi acel.



Cura me nongo katikati pa wel tunu anyogi ma tye ii m2 1.

Adwogi me kor tic pa Uno, Tad ka Mim tye eno.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Katikati me wel cam ma tye ka dongo pi lanyut acel acel.

T1 4 3 4 5 16 4

T2 5 6 0 5 16 4

T3 5 4 3 0 12 3

T4 2 6 5 3 16 4

T5 7 4 4 5 20 5

Katikati me wel cam ma tye kadongo/m2 4


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Wel tunu anyogi ducu me tye i .

Wel cam ma tye kadongo ducu.

Katikati me wel tunu anyogi pi lanyut acel acel.

T1 6 5 4 5 20 16 1.25


4 16 16 1


15 12 1.25

T4 3 5 5 3 16 16 1

T5 6 6 3 5 20 20 1

Katikati me wel tunu anyogi pi tyen anyogi acel acel 1.1

Tad ka Mim tye ki katikati me tyen anyogi 4/m2 ka dong avuereg me tunu anyogi 1.1 /tyen

anyogi acel acel.

Watyeko byeko katikati me wel tyen anyogi ma tye i

cikweya mita acel acel ka dong katikati me wel tunu

anyogi ma tye pi tyen anyogi acel acel.


17

Citep me 4: Byek wel tunu anyogi ducu ma tye i poto

Me agiki, me byeko katikati me wel tunu anyogi ma tye i poto, nya wel tunu anyogi /m2 ki ariya

me dit pa poto.

Ka ariya tye i hecta nyo ecka lok gi wek odok i m2. (hecta 1 = 10,000 m2 ; ecka 1 = 4,050 m2).

Wel tunu anyogi ducu ma tye ipoto = katikati me wel tunu anyogi/m2 x ariya pa poto i m2

Pi man, katikati me wel tunu anyogi/m2 pa lanyut magi = 4 x 1.1 = 4.4 tunu anyogi/m2.

Man ki tiyo kwede ma calo byeka pa katikati me wel tunu anyogi/m2 pi poto kulu.

Byeko wel tunu anyogi ducu ma tye i poto

Poto pa Tad ka Mim tye ha 1.23 = 1.23 x 10,000 = 12,300 m2.

Gin tye ki tunu anyogi 4.4/m2.

Pi meno, Tad ka Mim tye ki tunu anyogi 4.4 x 12,300 = 54,120 i poto ma megi.

Pi tyen lok me apora, tii ki kaac nyo cam ma ocek pi dit pa poto moni nyo ariya moni.

Wel tunu anyogi ma tye pi ha (hecta) acel, nyaa 4.4 ki 10,000 = tunu anyogi 44,000 pi

ha acel.

Wel tunu anyogi pi ecka acel (Kaac), nyaa 4.4 ki 4,050 = tunu anyogi 17,820 pi ecka

acel.

Roto lagam ma megi kun nongo cok-cok kwede.

NB: me byeko pek pa anyogi ma nyige, wot wa ilim me 11.

Me roto lagam ma megi: Wot idye poto ma megi ka inen ma cok labongo tic ki latwoke angwen nyo wot ii nukta - “W” .

1. Ngol byeka me wel tyen anyogi ii m2 acel acel, man cung ikom

lac kin citep ma megi (nen Buk me 1- Lim me 2). 2. Ngol byeka me wel tunu anyogi pi tyen anyogi acel acel kun

itiyo ki wangi. 3. Nyaa wel magi ka acel me nongo byeka ma pe twero bedo ka

kare tutwal pi m2 acel acel. 4. Rot me neno ni lagam ma meri cok cok ki lagam ma inongo

con ca.


18

Lapeny me atima pi cawa manok 4 – Byeko wel tunu anyogi ducu ma tye ipoto.


1 Lapur ocoyo piny adwogi me me tic magi ikare ma en tye ka kwanyo lanyut ki I 5, T1-T5, ma oaa ki i poto ma tye ha 1.5. Byek wel tunu anyogi ducu ma tye ii poto man.

Tecen Wel cam ma tye ka dongo (tyen anyogi) Wel tunu anyogi

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

T1 3 4 0 1 4 2 Cam ma tye kadongo pe

2


T3 1 3 2 1 2 2 2 1


2 3


3

2 Byek wel tunu anyogi ducu ma tye ipoto pa lapur ma tye ha 1 kun itiyo ki adwogi me tic magi ma ki coko ki ii T1-T5.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

T1 2 3 1 2 3 3 2 2

T2 4 1 7 2 5 2 4 3

T3 0 5 6 5 Cam ma tye kadongo pe

6 4 6

T4 4 7 6 7 6 6 5 7


2 6

3 Lapur ocoyo piny adwogi me lanyut me 3, T1-T3 kit man, ki i ha 1.25. Byek wel tunu anyogi ducu ma tye ipoto man.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


3 2 4




Cam ma tye kadongo pe

2 2

4 Lapur ocoyo piny adwogi me lanyut 3, T1-T3 kit man, ki i ha 0.6. Byek wel tunu anyogi ducu ma tye ipoto man.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


4


4 3 3



19

Tidi, poto ma pe rom- gin akwana mukene Kit ma ki nyutu kwede ii wel lanyut “ma cik yee ki kakwene ma lanyut myero kikwany ki iyee” meja me lakwong pi lim me 9, poto ma pe rom dok tino (ma pe oo ha 0.5) myero kipok woko iye ariyo nyo adek ma kilwongo kabedo ma tye ki cam ma tye ka dongo ki kit dongo gi marom.

But poto ma kabedo man cung pire myero byeka otime iye.

Kwanyo lanyut myero otime ii acel (lanyut agnwen) pi kabedo acel acel.

Katikati me cek pa cam ii m2 acel ileb me tunu anyogi nyo wel wii anyogi pi kabedo acel acel myero dong ki tim cura ne.

Katikati ma dong kityeko pimo pire pi poto ducu ki timo cura ne ki nyayo byek me cek pa cam ii m2 acel ki % (100) ariya ma kabedo acel acel orumu ka dong ki medo gi ka acel.

Labole, poto ma tye ha 0.4 me kabir tye cok cok ki % 60 pa ariya ma ka mege ma nen tye katimo maber dok kom gi yot ka % (100) 40 ma nen calo pe tye katimo ma ber. Poto man myero kipok woko i zon, kwed myero ki cok ki i lanyut ma tye i m2 1 kadong cura ki tim malube kit man.

Kabedo Wel cam ma tye ka dongo (tyen anyogi)

1 pi kabedo acel acel

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Wel tyen anyogi/cam ma tye kadongo ducu


Kabedo me 1 6 4 8 6 24 6

Kabedo me 2 2 1 3 2 8 2

Kabedo Wel tunu anyogi


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Wel tunu anyogi ducu kabedo acel acel

Wel tyen anyogu ducu ma tye i kabedo acel acel.

Katikati me wel tunu anyogi ma tye i tyen ayogi acel

Kabedo me 1 9 5 10 8 32 24 1.33

Kabedo me 2 1 1 2 2 6 8 0.75

Kabedo Wel tunu anyogi



Katikati me wel tunu anyogi pi tyen anyogi acel acel.

Katikati me wel tunu anyogi pi lanyut acel acel.

Ariya pa poto ma kabedo man tye iye.

Wel tunu anyogi ducu ma ki pimo

Kabedo me 1 6 1.33 6 x 1.33 = 8 60% 60% x 8 = 4.8

Kabedo me 2 2 0.75 2 x 0.75 = 1.5 40% 40% x 1.5 = 0.6

Pi meno, wel tunu anyogi ducu ma ki pimo pi m2 acel acel pi poto alutu = 4.8 + 0.6 = 5.4

Dit pa poto man tye ha 0.4 nyo m2 4,000.

Pi meno, wel tunu anyogi ducu ma ki byeko tye 5.4 x 4,000 = 21,600 i poto.



20

Lim pa Uno How me 10 i poto…Byeko wel cam ma tye ii citua nyo

dero cam



21

Dite

Dite- aye obedo kabedo ma gin moni pongo man twero bedo gin ma pige nyo ma tek – labole, dit pa kabedo ma nyig cam mayo ki i dero nyo pii ma tye iyi koc. Lapim ma padi padi ki tiyo kwede me pimo dit. Pi gin ma pige labole, ki pimo ii lace, boo ne (m3), Lita (l) nyo mililita (ml). Dit pa jami ma tego nyo ma pek (Nyig cam/ngom) dok tye ma dongo tutwal pi man ki pimo i lace, nyo boo ne (m3). NB: m3 1 = lita 1,000.

Lita 1 = ml 1,000. ml 1 = cm3 1 m3 1 = ml 1,000,000.

Cura me nongo dit pa nukta mogo ma yot.

Kabedo ma latwoke angwen ma rom nyo latwoke angwen ma pe rom = H x W.


Byeko wel cam ma tye ii dero

Pimo dit pa dero ma kit gi padi padi. Ki byeko wel dit pa dero ma megi ki tero pim me peke pa tunu anyogi ma tye I dero, Tad ka Mim twero byeko wel wel tunu anyogi ma gin gitye kwede i dero ma rom aroma ki pek pa nyig cam ma gin myero gutiny ki ii kom tunu anyogi magi. Man tere, byeko wel cam ma tye i dero mito nyango me timo cura me nongo dit pa dero ma kit padi padi.

Tad ka Mim tye ki tunu anyogi mogo ma gin ogwoko I dero. Gin tye kamito ngeyo nyig anyogi marom kwene ma gin binongo ki ikom tunu anyogi meno.


22

Ka wa tye kapimo dit pa jami, wa tiyo ki lapim ma nyute ki 3, labole, m3 nyo cm3 ma tere tye ni namba moni onyane kene kene tyen adek. Man pien ni dit pa jami myero ki wac pire ii kabeo adek mapat pat – bore, lace ki dong la male. Yoo me nongo dite cung ikom nukta. Nukta ma pol kare itwero rwate kwede aye:

Kiuboid: man nukta ma tye ki bute ma tye latwoke angwen pe rom: bute tye ma ocung atir ka dong ma twoke angwen ma rom nyo ma tye latwoke angwen ma perom. Labole aye bok, Kuret,dero munu, ki mukene. NB: Kiub en aye obedo gin ma twoke tye ma rom.

Cilinda: man tye ii nukta pa paipwo. Bute tye ma ocung atir ki dong doge ma tye aryo nyo ma olunge calo tong gweno. Labole aye dero, Karton,Kikobo,Paipwo ki dong Jag.

Pirizim: Bute ki bute tye ma ocung atir ki dong bute mukene nen calo latwoke adek. Ma lube ki dero me gwoko cam, nukta magi pol kare ki toro woko ki lace, ma calo wii dero.

Hemispia: Man obedo nucu pa gin ma obedo arot nyo atong gweno.(Nucu pa nukta pa odilo) labole, dero me gwoko cam ma tye olunge ma ki ngabo iwii purem.

Hemispirod: Nucu pa cipia ma ki daro. Labole: nyig cam ma ki onyo lobongo dilo ne idye ot.

Kon: man aye gin mo keken ma tye ki tere ma lac ma twero bedo ma olunge nyo arot ki dong pol kare cung keken ikabdo acel- Ki dong wiye bene tye ma ocwine. Man nen calo nyig kal ma kiduru ka kare acel kun nongo kitiyo kimalo.


23

Kiuboid – tye ki bute ma ocung atir ki ltwoke angwen marom nyo me nukta

latwoke angwen ma pe rom ka ineno ki ibute.

Lace tye ki latwoke angwen ma pe rom nyo latwoke angwen ma rom ki ku bute ka ineno arii.

Waneno kabedo pa nukta magi i Buk me 1 – Lim me 2. Kabedo ma latwoke angwen ma rom

nyo latwoke angwen ma pe rom = H x W.

Me nongo dit pa lace, myero wanya tung bute man ki bor pa lac meno.

Pi meno, yoo me timo cura me nongo dit pa lace aye:

Dite(Dwonge) = H x W x L

Labole: Kuret tye ki lamale ma tye cm 60, lace tye cm 50 ki dong bore cm 120. Dwonge pa

kuret man tye adii?

Dwonge = cm 60 x cm 50 x cm 120 = cm3 360,000

360,000 tye namba ma dwong tutwal pi man waloke me dok i m3. Tye million 1 cm3

(1,000,000) i m3 1. (100 x 100 x 100).

Pi meno, cm3 360,000 ÷ 1,000,000 = m3 0.36.

Yot tuwal me loko cm me doko m ma peya icako lanya ma ka megi. Man pien tye cm 100 ii m

1, itimo man ki poko daimencon ki 100:

cm 60 x cm 50 x cm 120 = m 0.6 x m 0.5 x m 1.2 = m3 0.36.

Pi man, dwonge pa kiuboid = m3 0.36.

Lapeny me atima pi cawa manok 5 – Dwonge pa kiuboid


Nong dwonge pa kuret man ii m3 (NB: cal man pe kigoyo ma rwate ki dit pa kuret man kikome) 1 2

3 Dero cam ma tye I nukta pa Kiuboid tye ki bore ma tye m 2, m 1 lamale ka dong lace tye m 0.5. Dwonge pa dero man tye adii i m3?

4 Nong dwonge pa dero man ma tye i nukta pa kiuboid (i m3) ma bore tye m 3, lamale tye m 1.5 ka dong lace tye m 0.6.


24

Cilinda – tye ki iye ma twolo dok arot nyo olunge ki bute ducu ma tye ma ocung atir

Cylinda tye ki iye ma twolo dok olunge. Weno pi jami olunge (Lawala) i Buk me 1 – Lim me 4, Ka itye ka timo cura me nongo ariya pa ot lum alunga ka odi ma tye ka ma poto orumu. Ariya pa lawala (Ka bedo nyo jami ma olunge) = π x r2 (π = 3.142). Me wek inong dwong pa cilinda, wa nyayo ariya pa tenge ki lamale (H) pa cilinda meno. Pi meno, yoo me nongo dwong pa cilinda aye:. Dwonge = πr2 x H (nyo L). NB: L= Bore ka H = Lamale Labole: Cilinda ma tye ii nukta pa paipwo tye ki radiac(r) me cm 20 ka lamale (H) me cm 50. Lapur mito ngeyo dwong pa cilinda man i lita.

Dwonge pa paipwo = 3.142 x 202 x 50 r2 = 202 = 20 x 20 = 400 Dwonge = 3.142 x 400 x 50 = cm3 62,840. (kit ma cm3 1000 = lita 1). Pi man, cm3 62,840 = 62,840 ÷ 1,000 = lita 62.84.

Pi man, dwonge pa barel nyo paipwo = cm3 62,840 nyo lita 62.84

Lapeny me atima pi cawa manok 6 – Dwonge pa cilinda.


Nwong dwonge pa cilo (i m3) (NB: pe ki goyo ma rwate ki di pa cilinda man ki kome): 1 2 3

4 Koc ma tye ki lamale ma tye ki cm 25 ki radiac ma tye cm 10. Dwonge pa koc man tye adii ii cm3? 5 Jag ma tye ki lamale ma tye cm 20 tye ki diamita ma tye cm 10 (wii opo ni radiac tye nucu diamita ). Dwonge pa jag man tye adii ii cm3?


25

Pirizim – Ka ineno arii nen calo traengul ma tye ki bute ki bute ma tye rektengul Prism 1 Prism 2

Arii ne nen ma calo traengul. Watimo cura me nwongo ariya pa traengul ii Buk me 1 – Lim me 2. Fomila me nongo ariya pa traengul = ½ x B x H

Me nongo dwonge pa pirizim ma obedo traengul, wanyayo ariya ma nen ki tung bute ki bor ma

mege.

Pi man, Fomila me nongo dwonge pa pirizim aye:

Dwonge = ½ x B x H x L

Labole, ka pirizim 1 ma maloni, ter traengul = cm 10, lamale = cm 20 ka dong bore = 100 cm,

Dwonge = ½ x 10 x 20 x 100 = cm3 10,000 = ml 10,000 = lita 10.

Nyo pien m3 1 = cm3 1,000,000 man rom aroma ki 10,000 ÷ 1,000,000 = m3 0.01.

Pi man, dwonge pa pirizim = cm3 10,000 nyo m3 0.01 nyo lita 10.

You are likely to find prisms forming the top part of a crib, which if filled to the top will include the prism.

Lapeny me atima pi cawa manok 7 – Dwonge pa pirizim


Nong dwonge pa pirizim magi (NB: cal man pe ki goyo ma rwate ki dit pa pirizim magi kikome):

1 2

3 Nong dwonge pa dero. Man obedo pirizim (ma tye ki rait angul traengul) ma otore ki kiuboid (man bene pe ki goyo ma rwate ki dit pa dero man ki kome)


26

Hemicpia – nucu pa cipia

Cipia obedo calo odilo – hemicpia obedo nucu pa cipia.

Fomila me nongo dwonge pa cipia = 4/3 π r3 = 4/3 π x r x r x r.

Pien hemicpia obedo nucu pa cipia, fomila me nongo dwonge pa cipia aye:

Dwonge = ½ x 4/3 π r3 ma en aye 2/3 π r3

Pien cam ma nyige cer me dok piny ma lube pek ma megi, man weko gin pol kare yubu

hemicpia, kono kace pe gin mo ojolo nyig cam man ki piny.

Labole: Nyig cam ma ki duru ma ocung ki tung wiye tye cam ma odure ma radiac mere tye

m 1:

Volum pa cipia pa cam ma odure dok ocung ki wiye ni = 2/3 π r3 2/3 x 3.142 x 13 = 0.66 x 3.142 x 1 x 1 x 1 = 0.66 x 3.142 x 1 = m3 2.07

Pi man, dwonge pa hemicpia man tye m3 2.07 ma ki twero raunding me bedo m3 2.

Hemicpirod – tye nucu pa cipia ma ki bapu. I labol ma tye piny eni, wii kabir ki tye ka duru ki ii citua ii nukta pa hemicpia. Cam ma ki duru I nukta pa hemicpia tye ma nongo obap loyo hemicpia, ki dong makato radiac gip e rom rom ii direkcon ducu.


27

Kon – man obedo gin ki bute ma olunge nyo arot ma yubu kabedo iwii dyere pa

tere.

Yoo me nongo dwonge pa kon = 1/3 π r2 h.

Labole, Kon ma tye ki radiac me m 1 ka dong lamale ma tye m 0.5. Lapur mito ngeno dwonge ma i m3.

Dwonge pa kon = 1/3 x 3.142 x 12 x 0.5 = m3 0.52.

Ka ce watiyo ki r1, r2 ka r3: kun nongo r1= lamale (H), r2 aye radiac ma bor ka dong r3 aye radiac macek pa cam man kiduru.

Dwonge = 2/3 π r1 x r2 x r3

Labole, cam ma kiduru tye ki lamale ma tye 0.5 m (r1), radiac mabor ma tye m 2 (r2) ka dong radiac ma cek ma tye m 1 (r3). Dwonge = 2/3 π x r1 x r2 x r3 = 2/3 x 3.142 x 0.5 x 2 x 1 = 0.66 x 3.142 x 1 = m3 2.07.

m3 2.07 wa twero raunding me dok piny cidong bedo m3 2.


28

Lapeny me atima pi cawa manok 8 – Dwonge pa hip (Cam ma kiduru)


Dok cen i lim pa Uno How me 10 i poto

Nong dwonge pa hip magi (NB: pe kigoyo ma rwate kid it pa hip magi ki kome): Lapeny me 1, 3, 4 ki 6 obedo kon; lapeny me 5 obedo hemicpia. 1 2

3 4

5 6


29



Pimo dwonge pa cam ma pe ki dino ma tye i citua.

Dero acel pa Tad ka Mim tye kinyutu piny eno.

Ki yubu ma calo kiuboid ma tye ki pirizim ma obedo traengul ki tung wiye. Cura me nongo Dwonge pa nukta ariyo magi twero tiye ento pat pat ka dong wa medo gi lacen. Wi opo ni, fomila me nongo dwonge pa kiuboid = W x H x L Kiuboid tye ma lace m 0.6, m 1.5 malo ka dong bore tye m 2.5.

Dwonge pa kiuboid = m 0.6 x m 1.5 x m 2.5 = m3 2.25.

Wi opo ni, fomila me nongo dwonge pa pirizim ma obedo traengul = ½ x B x H x L

Pirizim ma bore tye m 2.5 ki ariya me kroc cekcon ma tye ki rait angul traengul, tye ki tere ma lace tye m 1.

Tad ka Mim gwoko anyogi gi ma otegi dok kitwoyo

maber ni ki tunu gi ducu i dero gi ma kiyubu ki bao ni.

Gin tye ki miti me nongo dwonge pa dero ma megi

man.


30

Dwonge pa pirizim = ½ x m 0.6 x m 1 x m 2.5 = m3 0.75.

Totol dwonge pa dero man = dwonge pa kiuboid + dwonge pa pirizim.

Totol dwonge pa crib = m3 2.25 + m3 0.75 = m3 3.

Pi man, dero pa Tad ki Mim dite tye m3 3

Tad ka Mim tye ki dero aryo, dero magi tye ki cac wa ki nukta ma megi ma cal cal. Pi man , totol me dwonge pa dero magi = 3 + 3 = m3 6.

Lapeny me atima pi cawa ma nok 9 – Dwonge pa dero.



Nong dwonge pa dero magi (NB: pe kigoyo ma rwate ki cac dero magi ki kome) 1

2


31



Byeko wel tunu anyogi nyo wiye i dwonge ma ki miyo.

Ka dong watyeko nongo dwonge pa dero ma megwa,

dong watwero byeko wel tunu anyogi ducu na tye iyi

dero ki kwanyo lanyut me wel ki rom roma I kabedo

ma pat pat.Me timo man, wamito koc matino ma

wangeyo dwonge (labole; koc me lita 20).

Tad ka Mim tye ka kwanyo lanyut pa tunu anyogi ki I dero ma megi me konyo byeko wel tunu ma tye i dero. Ma rom aroma ki lanyut ma kikwanyo ki i poto, lanyut man myero ki kwany ataa lobongo neon ne. Itwero neno ni lanyut ma megi tye ma rwate kun nongo ilubu yoo magi.

1. Pong cam I dero ma rom aroma i nino aceli.

Ka dero ma megi tidi: Ki iwii, pok dero ma megi iye angwen atir atir man kilwongo bute. Mii namba ki bute acel acel. Co namba magi I karatac ka dong ikwany bute ma imito kwanyo lanyut ki iye labongo neno ne. Ki diro, kwany lanyut me tunu ki I bute magi.

Ka dero tye ma dit ento ki pongo cam iye inino aceli: Pok dero man iye 4 atir atir ka dong mi gi bute magi namba. Kwany bute ma ibino kwanyo lanyut ki iye labongo neno ne. pok dok bute magi arii man kilwongo bute matidi, pok dong namba magi dong pot bute acel acel, ka dok aye kwany namba acel ataa labongo neno ne. Ki diro, kwany tunu anyogi ducu ma tye i bute matidi man ma calo lanyut ma ka megi.


32

ITIC ACEL ACEL

Ka dong ityeko kwanyo lanyut ma ka megi, oony gi i kapet wek odure ma nen calo tunu layata.

Rub dure man ma ber, ka dong ipoke iye angwen.

Labongo neno ne, kwany acel me angwen ka dong itii ki wel tunu anyogi magi ma calo lanyut ma ka megi.


Tad ka Mim otyeko yero lanyut ma ka megi me tunu anyogi ka dong ka dong gin oketo ii koc ma dite tye liat 20 iyoo acel kit ma nongo kicano gi kwede idero ca. Tad ka Mim ocano tunu anyogi 50 ii koc man ma tye lita 20 ni.

2. Dero ma kipongo ki cam ma oaa ki ipoto ma pat pat ki dok bene inino ma pat pat.

Ka dero ki pongo inino ma pat pat nyo ki cam ma oaa ki ipoto ma pat pat, omyero ikwany tunu anyogi ibut dero ducu, pe keken ki i cekcon acel keken.

Kit ma con ca, pok citua iye 4 atir atir. Kombedi kwany koc acel me tunu anyogi nyo wii cam ki ii cekcon ducu – yab dero ka irwak koc arii ii ikin tunu anyogi wii cam ma odure ii cekcon meno. Rwak cingi iye me kony pongo koc man ka dong iwote woko ma nongo dong opong ki tunu anyogi nyo wii cam.


33



Byeko wel tunu anyogi ducu ma tye ii citua.

Tad ka Mim ngeyo ni tunu anyogi 50 donyo i lita 20. Dero gi ducu opime tye m3 6 ento kit ma dwonge pa koc ki tito pire ii lita ni, myero pin olok dwonge pa dero ma megi ni woko ii lita. Me nongo koc adii ma donyo ii dero man, myero gin opok dwonge pa dero man ki dwonge pa tin. Koc acel = lita 20. Dero ariyo = m3 6 = lita 6.000 tere niya, dero ariyo tero 6,000/20 = koc 300. Kit ma koc acel acel tero tunu anyogi 50, dero man tingo tunu 300 x 50 = 300 x 50 = tunu 15,000.

Lapeny me atima pi cawa manok 10 – Wel tunu anyogi ducu ma tye ii citua.



Ngeno tunu anyogi adii ma tye ii koc me lita 20,

watwero byeko wel tunu anyogi ducu ma tye icitua, ki

bene ka wangeyo dwonge pa citua.

1 Lapur tye ki koc ma dite tye lita 10. En odilo tunu anyogi 18 iye, ma ki kwanyo labongo yero ne ki ii dero ma mege, ka oketo gi ikoc man. Dero ma mege dite tye m3 2 dok tye ma opong. En dong tye tunu anyogi ma romo adii idero ma mege man?

2 Lapur tye ki koc ma dite tye lita 20. En odilo tunu nyogi 34 iye, ma ki kwanyo labongo yero ne ki ii dero ma mege, ka oketo gi ikoc man. Dero ma mege dite tye m3 5. Dero man opongo nucu ne keken. En dong tye tunu anyogi ma romo adii idero ma mege man? 3 Lapur tye ki koc ma dite tye lita 10. En odilo wii kabir 30 i koc man ma okwanyo labongo neno ne ki idure ma kabir ma megi. Dure me kabir ma mege man tye m3 2. En dong tye wii kabir ma romo adii idero ma mege man?

4 Lapur tye ki koc ma dite tye lita 20. En odilo wii Kal 50 ii koc man, wii kal magi en okwanyo labongo neno ki dure me kal mere, Dure me wit kal mabn tye m3 1. En dong tye wii kal ma romo adii idero ma mege man?


34

Yubu maleng ki tinyo dul kom cam ma ki kwanyo ki i poto. Pi anyogi, kabir ka kal, nyig gi myero ki kwany woko ki iwii gi nyo itunu ma megi ki tinyo nyo dino. Tiny/din ka ikwor woko kom cam ma ikayoni kit ma lapur timo kwede con. Teme ki tek me neno ni idwoko piny rweny pa nyig cam ka itye ka tinyo nyo dino gi. Pimo pek pa jami.

Kilo pol kare kitiyo kwede me pimo pek pa lanyut ducu ma ki kwanyo. Ma pud peya pim otime, kilo myero ki ter ocung i zero kun nongo ki golo kica maleng ma iye nono. Tim man ka ma ogenge ki ikom yamo ma kodo.



Pimo pek lanyut me cam.

Tad ka Mim otinyo ka opimo nyig anyogi ma gin con ca odilo i koc. Nyig cam ma ki tinyo ki i lita 20 me tunu anyogi otelo kig 3.8. Dok cen i lim pa Uno How me 10 i poto

Kom bedi kit ma dong ityeko byeko tunu anyogi

ma tye idero ni, itwero bene byeko wel nyig cam

ma tye idero ma megi. Cak ki tinyo lanyut me tunu

anyogi ma ikwanyoni ka dong ipim ki kilo.

Nyig kaodi myero ki ket i kica maleng, ki pim ka dong wel kilo magi ki coyo piny. Ka lanyut man tye ma dit,twero mite ni ki pim i dul ma pol

ka dong pek gi ducu ki medo ka acel agiki me pim magi.


35

Tad ka Mim mito byeko pek pa nyig ma gin bino bedo kwede ka gin otinyo anyogi ma megi ma tye ii dero ma megi. Dwonge pa dero man tye m3 6 = lita 6,000. Gin dong otyeko timo cura ka gunongo ni tye cok cok 300 me tunu anyogi ma tye idero ma megi. Nyig cam ma oaa ki i koc acel otelo kilo 3.8 Pi man, nyig cam ma oaa ki i koc 300 byeke ni: kg 3.8 x 300 = kg 1,140. Pi man, Tad ka Mim tye ki ngec me nongo kg 1,140 me nyig anyogi ma aa ki ikom tunu anyogi ma tye idero ma megi. Me loko man me dok i tan (MT), pok wel kilo man ki 1,000 = kg 1,140 ÷ 1,000 = tan 1.14.



Tic ki pek pa lanyut me byeko pek pa cam ducu ma tye i dero.

Lapeny me atima pi cawa manok 11 – Byeko pek pa cam ma tye i dero ni aa ki i pek pa lanyut pa cam ma ki kwanyo.


1 Lapur tye ki dero ma obedo lace ma lamale tye m 1.2, bore tye m 1 ka dong lace tye m 0.5. Tye ma opong ki tunu anyogi. En okwanyo lanyut pa tunu anyogi magi ka odilo ii koc ma dite tye lita 10. En odilo tunu anyogi 15 ii koc man. Ki inge tinyo gi, nyig anyogi magi ducu otelo kg 0.6. Lapur ma dong kono tye ki tunu anyogi ma romo gin adii idero ma megi ki dong ki dong

tunu anyogi magi ducu twero telo kilo adii?

2 Dero pa lapur ki yubu ma tye kiuboid ki pirizim. lace lamale tye m 2, m 3 bore ka dong m 1 lace. Pirizim tye ki tere ma lace tye m 1, bore m 3 ka dong lamale tye m 1. Dero man tye ma opong woko ki tunu anyogi. Nyig anyogi ma ki kwanyo ki ii koc lita 20 otelo kg 2.5. Lapur man tye ki tunu anyogi adii i dero ma mege ki dong nyig anyogi ma romo kilo adii

ma gin bino nongo?


36

Nyig cam ma pat pat tye ki l peki gi ma pat pat. Meja ma tye piny eni nyutu pek pa cam ma pol kare ki puru gi.

A1 = pek i kg/lita A2 = pek i tan/m3 B = pek i kg/m3

Nyig kabir 0.62 0.62 620

Ngor 0.74 0.74 740

Lapena 0.75 0.75 750

Pul, ma golo 0.30 0.30 300

Pul, ma nyige 0.64 0.64 640

Anyogi (ma nyige) 0.72 0.72 720

Kal 0.63 0.63 630

Muranga 0.76 0.76 760

Nyim 0.59 0.59 590

Kabir 0.73 0.73 730

Canpulowa 0.42 0.42 420

Nyig Wiit 0.77 0.77 770

Wel magi twero loke ma lube ki ngico ma tye i cam, Kit cam moni, ber pa cam, rwom me cilo ma tye i cam ki mukene. Man pole pe tye ka kare tutwal ento pud pire bene tek mada me byeko cek pa cam nyo kaac.

Kede ka bed ipe ki kilo me pimo jami, yoo mo tye ma pud itwero byeko ki pek pa cam ma megi ni aa ki ii dwonge pa koc kun itiyo ki peke. Peke obedo pek pa dwonge acel acel pa nyig cam mo keken ma pe odile. Nyano bal denciti pa nyig cam ma calo meno ki dwonge ma itye kwede, itwero byeko dwong pa nyig cam ma tye I dero, ki ka ingeyo dit pa poto ma kaac otime ki iye, itwero timo cura me nongo kaac ma twero kati ki i eka acel acel.

Tic ki pek me byeko pek pa cam ma tye i dero.

Tad ka Mim kono nongo gu nongo pek pa cam ma ka megi ki nyayo dwonge pa cam ma ki tinyo ki pek pa anyogi. Anyogi ma kitinyo ki ikom tunu 50 opongo nucu pa koc ma tidi ma dite tye liat 10 – cok cok ki lita 5. Me nongo pek pa lita 5 me nyig anyogi, wa nyayo dwonge ki peke. Pek pa nyig anyogi tye 0.72 kg/l. Man tere niya, ii katikati, lita 1 me nyig anyogi telo kilo 0.72 x 5 = kg 3.6. Man obedo namba ma cok cok ki 3.8 ma Uno otimo cura ne kun tiyo ki pimo nyig cam man ii kilo. Wii opo ni, tiic ki bal denciti pe miyo adwogi ma kakare ma kato pimo jami ki kilo ento kede ka bed kumeno, pud pire tek dok kony me nyuti wan yoo.


37

Lapeny me atima pi cawa manok 12 – Cura me nongo pek pa cam ma tye i dero kun

watiyo ki pek ma ki tiyo ki koc.



1 Lapur tye ki kuret ma opong ki tunu anyogi, kuret man lamale tye m 1, bore tye m 0.8 ka dong lace tye m 0.4, lanyut pa tunu anyogi man gin 28 opongo koc ma dite tye lita 20. Kare ma tunu anyogi man ki tinyo, nyig anyogi man opongo 1/5 pa koc man ma dite tye lita 20 ni. Dong tong tunu anyogi adii ma lapur man tye kwede ii dero ma mege? Kun itiyo pek pa anyogi, byek wel kilo pa nyig anyogi ma dero man tye kwede.

2 Lapur tye ki dure me tunu anyogi ma nen calo hemicpirod ma ki onyo ingom ma dite tye m 1.6 x m 0.8 x m 2. Tii ki bal denciti ma kimiyo con ca me byeko pek pa nyogi ma witi (ma pe ki tinyo).

3 Lapur tye ki dero ma tye ki dwonge me m3 2.5. Dero man tye ma opong ki kabir ma witi.

En dong okwanyo lanyut me wii kabir 50, ma obongo koc ma dite tye lita 25 ka odino gi

woko. Nyig kabir ma oaa ki ikom wii kanir 50 magi opongo ½ pa koc ma dite tye lita 5.

Kun itiyo ki bal denciti pa kabir, byek wel kilo me nyig anyogi ma dero man tye kwede.


38

Lim pa Uno How me 11… Byeko cek pa nyig cam ma pud tye i poto.



39

Uno oniang ni lyro tye ki cam ma opike, poto ma mere neni tye ki cam ma pol pi ariya acel acel ma tye ipoto gi makato poto pa Tad ka Mim. Cal ma tye piny eni nyutu cam ma pek ma malo (opike) ki pek ma piny (pe opike)

Pek ma malo Pek ma piny.


Byeko nyig cam ma tye ka dongo i poto Pek pa cam (wel cam ma tye kadongo).


Pek pa cam obedo wel cam ma tye ka dongo ii ka bedo moni.

Ka wel cam am tye ka dongo ikabedo moni tye

lamal en aye miyom kiwan cam ma dwong ii

kabedo ni


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Iyro mito byeko wel tunu anyogi ki pek pa nyig anyogi ma en bino nongo ki ikom cam ma en peya okayo. Kit ma con, yoo me acel aye me byeko wel cam ma tye kadongo ki dong tunu anyogi ma tye ii m2 acel acel kun nongo watiyo ki latwoke angwen. Wel tyen anyogi ma tye ii lanyut man ki wel tunu anyogi ma tye ii lanyut man myero ki kwan ka

ki co piny ii meja, man cal cal ki ma Tad ka Mim otiyo kwede con caa.

Ka lanyut kitye ka kwanyone, anyogi ducu myero kicok ka ki gur gi I oduu ne.


Byeko nyig cam ma tye ka dongo i poto Kwano tunu anyogi ki cam ma tye kadongo (Kwan odoco/Lapoo wiic).

Iyro,Tad ka Mim okwanyo lanyut ki ipoto pa lyro, gin okwano wel tyen ki tunu anyogi, kun gin tiyo ki yoo acel ma con caa (Nen lim me 9). Adwogi me tiic man kinyutu pire ii meja ma tye piny.

Tecen Lanyut me 1 (m2 1) Lanyut me 2 (m2 1) Lanyut me 3 (m2 1) Lanyut me 4 (m2 1)


Wel tunu anyogi


Wel tunu anyogi


Wel tunu anyogi


Wel tunu anyogi


7 14 6 12


6 11 4 10 4 7


4 8

T4 5 10 1 2 3 6 4 8

T5 4 6 6 11 5 8 5 5



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Iyro kombedi mito nongo katikati me wel tunu anyogi/m2 i lanyut magi.


Byeko nyig cam ma tye ka dongo i poto

Byeko well tunu anyogi ma tye i m2 1 (Lapoo wiic). Kit ma okwongo con, me timo man, en mite me nongo wel katikati pa wel cam ma tye kadongo pi m2 acel acel ka dong wel katikati me wel tunu ma tye I tyen anyogi acel acel.

Katikati me wel tyen anyogi ma tye i m2 acel:

Katikati ducu ki pete tere pa cam me tye kadongo/m2 = (4.5 + 3.5 + 3 + 3.25 + 5) ÷ 5 = 19.25 / 5 = 3.85

Wel tunu ma tye ityen anyogi acel acel:


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Totol me wel tunu anyogi ducu ii acel acel

Totol me we tyen anyogi ducu ma tye ii

Katikati me wel tunu anyogi ma tye ikom tyen anyogi acel acel


14 12 36 18 2


11 10 7 28 14 2


8 24 12 2

T4 10 2 6 8 26 13 2

T5 6 11 8 5 30 20 1.5

Katikati ducu ki pete tere pa tunu anyogi ma tye ityen anyogi aceln = (2 + 2 + 2 + 2 + 1.5) ÷ 5 = 9.5 / 5 = 1.9 Wel tunu/m2 = katikati me welt yen anyogi/m2 x katikati me wel tunu anyogi/tyen anyogi = 3.85 x 1.9 = tunu 7.31/m2 Pi man, katikati me wel tunu anyogi ma tye i m2 acel pi lanyut ma ki kwanyo ki i poto pa Iyro

ni = cok cok ki tunu 7/m2

Man ki tiyo kwede ma calo byeka me katikati me wel tunu anyogi ma tye i m2 1 pi poto ducu.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Katikati me wel cam ma tye kadongo/m2

T1 5 0 7 6 18 4.5

T2 0 6 4 4 14 3.5

T3 3 5 0 4 12 3

T4 5 1 3 4 13 3.25

T5 4 6 5 5 20 5


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Lapeny me atima pi cawa manok 13 - Katikati me wel tunu anyogi nyo wii cam ma tye/m2.



1 Lapur okwanyo lanyut ki ipoto ma dite tye ha 1 ka ocoko ngec ma tye piny eno:


Wel tunu anyogi

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

T1 1 3 2 3 1 3 4 5



5 4 4


3 5


6 5 3

Byeka me wel tunu anyogi ma tye ipoto pa lapur man tye adii?

2 Jami magi aye kicoko ikare me kwanyo lanyut ki ii poto kal ma dite tye ha 0.5:


Wel wii kal

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

T1 6 2 4 5 6 2 3 5

T2 8 5 6 3 7 4 6 3


2 4


3


1 5 2

Byeka me wel wii kal ma tye ipoto pa lapur man tye adii?

3 Jami magi aye kicoko ikare me kwanyo lanyut ki ii poto kabir ma dite tye ha 1:


Wel wii kabir

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


16


9 12

T3 14 16 15 9 14 16 15 9


8 14 18


13 9

Byeka me wel wii kabir ma tye ipoto pa lapur man tye adii?


43

Iyro mito byeko pek pa nyig ma oaa ki ikom tunu ma pod tye ipoto. En dong otyeko byeko

katikati me wel tunu anyogi ma tye ii m2 acel. Pi man, ka en twero byeko katikati me wel kilo

nyo pek pa nyig kodi ma aa ki ikom tunu acel pa lanyut ma ka mege, en bene twero byeko

pek pa nyig cam ma tye ii m2 1, ki bene pi poto alutu.

Me timo man, en myero okwany tunu anyogi ma en obedo ka kwanyo lanyute ni ka dong oket

gi idure. Dure man kipoko iye ariyo kadok iye ariyo magi dok ki poko iye .ariyomukene ka

dong ki kwany acel labongo neno me cung calo lanyut ma tidi.

Tunu anyogi ma oaa ki ii dure man ki kwanogi, ki tinyo ka dong nyigi ki pimo ii kilo.

Pek pa nyig kodi man ki nongo ki pimo ikilo, ka dong kipoko wel kilo man ki wel tunu anyogi

ducu ma ki tinyo me nongo wel kilo me nyig anyogi ma tunu acel acel okelo.



Byeko pek nyo pa nyig cam ma oaa ki i tunu anyogi nyo wii cam acel.

Me nongo wel nyig cam ma aa ikom tunu nyo wii cam acel:

Kwan tunu anyogi ma tye ii lanyut acel

Tiny nyo bit anyogi me lanyut man ka ipim

Pok pek pa nyig kodi man ki wel tunu anyogi ma ki tinyo.


44

Lanyut pa Iyro tye ki tunu 36. Nyig anyogi ma oaa ki ikom tunu 36 otelo kg 2.15. Pi meno, katikati me pek pa tunu acel acel me lanyut ma mege = 2.15 ÷ 36 = kg 0.059. g 1000 = kg 1, pi man nyig kodi ma oaa ki ikom tunu acel acel tye g 59.

Lapeny me atima pi cawa manok 14 – Pek pa nyig cam ma oaa ki ikom tunu acel nyo wii anyogi acel.



1 Lapur okwanyo lanyut me wii kabir 50. Nyig kabir man otelo kg 2.7. Byek pek pa nyig kabir man ma oaa ki iwi kabir acel.

2 Lanyut me dure kal ma tye k iwi kal 21 ki dino. Lapur pe ki kilo mo keken ento tye ki koc ma dite tye lita 0.5 ki bene ngeyo ni pek pa kal tye kg 0.63/l. nyig kal man opongo koc man lawang acel. Byek pek pa nyig kodi ma oaa ki iwii kal acel acel (i g).

3 Lapur okwanyo lanyut ki ha 2 me poto anyogi mere ka ocoko tunu annyogi 160. Opoko

man woko ka otinyo tunu anyogi 40. Nyig anyogi man opongo koc ma dite lita 2.5.pek pa

anyogi tye kg 0.72/l.

Byek pek pa nyig anyogi ma tunu acel telo (i g).

4 Lanyut ki kwanyo ki i poto ma dite tye ha 1 ka dong tunu anyogi 60 ki coko ki iye. Lapur opoko dure me anyogi man ka otinyo tunu 15 me anyogi man. Nyig anyogi man opongo koc ma dite tye 400 ml tyen 3. Bal denciti pa anyogi tye kg 0.72/l. Byek pek pa nyig kodi ma oaa ki ii tunu anyogi acel (i g).

5 Lapur okwanyo lanyut ki ipoto kal ma mege. Odino wii kal 80. Nyig kal ma oaa ki iwii kal magi opongo koc ma dite tye lita 1 acel tyen 1 ¼. pek pa kal tye kg 0.63/l. Byek pek pa nyig kodi ma oaa ki ii wii kal i acel (i g).

6 Lapur okwanyo lanyut ka oguru wii kabir 460 ii dure. Dure man ki poko apoka dong wii kabir 120 ki dino. Nyig kabir ma okati opongo koc ma dite tye lita 0.5 tyen 6½. pek pa kabir tye kg 0.73/l. Byek pek pa nyig kodi ma oaa ki ii wii kabir acel (i g).


45



Byek pek pa nyig kodi ma okati ki ii m2 1 ma pur otime iye. Iyro otyeko byeko ni katikati me g 59 kati ki ikom tunu anyogi acel cel. En bene obyeko ni katikati me tunu anyogi 7 kati ki ii m2 acel acel. Pi man, pek pa anyogi ma oaa ki m2 1 tye = 59 x 7 = g 413 /m2. Iyro tye ki nyig anyogi maromo g 413 nyo 0.41 kg/m2 nyo tan 4.13 /ha.

Lapeny me atima pi cawa manok 15 – Nyig cam ma tye i m2 acel.



Me byeko wel nyig kodi ma okati ki ii m2 acel acel ma pur otime iye.

Nyaa wel kilo pa cam ma okati ki ikom tunu anyogi

acel ki byeka me wel tyen anyogi ma tye ii m2 acel

acel.

1 Lapur okwanyo lanyut ki i poto ha 2 me poto anyogi ma mege ka oguru gi I oduu. En opoko oduu man ka otinyo tunu anyogi 40. Nyig anyogi man otelo g 3,600. Ki dong en bene otimo cura ka onongo ni itye ki tunu anyogi 4 pi m2 acel acel. Anyogi ma rom kwene ma lapur man tye kwede i m2 acel acel me poto mere.

2 Lapur okwanyo lanyut ki ipoto kabir mere ma tye ha 0.75 ka oketo gi idure. En tye ki wii kabir 68. En opoko dure me nyig kabir man ka odino wii kabir 17. Nyig kabir man otelo g 510. En dong otimo cura ka onongo ni itye ki wii kabir 3 pi m2 acel acel. Nyig kabir ma rom kwene ma lapur man tye kwede pi m2 acel me poto mere?

3 Poto ma dite tye ha 0.3 ki kwanyo lanyut ki iye ka kiketo gi I oduu.Lapur man opoko oduu me cam man ka otinyo tunu 62 me anyogi man. Nyig anyogi opongo koc ma dite tye lita 25. Kun itiyo ki pek pa anyogi (0.72 kg/l), tii cura me nongo pek pa nyig anyogi ma oaa ki ikom tunu acel. Ka lapur tye ki ngec ni en itye ki tunu anyogi ma romo 4 i m2 acel acel, nyig anyogi ma rom kwene ma lapur man tye kwede i m2 acel acel me poto ma mege.


46



Byeko pek pa nyig kodi ma tye i poto.

Kombedo ma dongo lyro otyeko byeko dwong pa nyig cam ma aa ki ii m2 acel, en dong twero timo cura me nongo byek pa cam ma cek ki ii poto mere ma dite tye ha 0.5. En dong otyeko nongo ni kaac ma mege dong tye kg 0.41/m2. Tye m2 10,000 i heckta (ha) acel. Pi man, byeka me kaac ma mege tye kg 0.41 /m2 x 10,000 m = kg 4,100 /ha. Poto pa lyro tye 0.5 ha, man tere ni en twero nongocam ma dite tye 4,100 x 0.5 = kg 2,050 ki poto mere. Man rom aroma ki tan 2.05. Kace lyro tye ki miti me poro poto mere ki meg pa Tad ka Mim, en twero timo cura ma kamere i tan/ha. Poto mere tye kg 4,100 /ha = tan 4.1/ha. Kaac me anyogi ma oaa ki ipoto pa Tad ka Mim obedo tan 2.3/ha. Pi meno, poto pa lyro obedo ki rwom me ceko cam maber loyo kit ma gin otamu pire con.

Lapeny me atima pi cawa manok 16 – Pek pa nyig cam ma tye i poto

Me byeko pek pa nyig kodi ma aa ki ipoto:

Nyaa wel katikati pa cam ma aa ki m2 acel x ariya me

dit pa poto meno.

1 Lapur ocoko ngec magi ikare tye ka kwanyo lanyut ki ii poto anyogi mere ma tye ha 1:


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

T1 5 4 6 3 4 5 5 4


4 5 3


3 2

T4 2 3 3 1 2 4 4 2 T5 1 0 4 4 2 Cam ma tye

kadongo pe 5 2

Tunu anyogi ki duru gi ka acel ka ki poko. Pek pa nyig kodi ma oaa ki idure acel ma tye iye ki tunu anyogi 15 obedo g 1000. Nyig anyogi ma rom kwene ma lapur man myero obed ki gen me nongo ki ii ha 1 me poto ma mere ni?


47

Lapeny me atima pi cawa manok 16 – Pek pa nyig cam ma tye i poto omede…


Byeko pek pa nyig cam ma tye ipoto matino, dok nongo poto man pe tye ma rom – gin akwana ma ki medo. I lim me 9, wa tito ni katikati me wii cam nyo tunu anyogi ma tye ipoto wa twero timo cura ne pi poto ma pe rom dok tino. Me nongo adogi ma ber, pire tek me kwanyo lanyut ki ii kabedo ariyo ma padi padi. Me mede ki I kom lobol ma con caa.

Kabedo Number of cobs

( 1 pi kabedo acel).

Wel katikati me tunu anyogi pi m2 cael

Katikati me pek pa nyig anyogi pi tunu acel (Ki nongo ki i kom lanyut ma ki tinyo)

Katikati me pek pa nyig cam pi m2 1 me lanyut

Ariya me dit pa poto ma zon okwako (orumu)

Katikati me pek pa nyig cam ma ki ki pimo pi m2 acel

Kabedo me 1.

6 x 1.33 = 8 g 40 8 x 40 = g 320 60% 60% x 320 = g 192

Kabedo me 2.

2 x 0.75 = 1.5 g 20 1.5 x 20 = g 30 40% 40% x 30 = g 12

Pi man, katikati me pek pa cam ma ki pimo ki ii m2 1 ki i poto ducu =

g 192 + g 12 = g 204 nyo cok cok ki kg 0.2.

Poto man tye ha 0.4 nyo m2 4000.

Pi man, tye byeka me 0.2 x 4,000 = kg 800 pa nyig cam ipoto man.


2 Lapur ocoko ngec magi ikare tye ka kwanyo lanyut ki ii poto kal mere ma tye ha 1.5:

Tecen Wel cam ma tye ka dongo (tyen anyogi) Wel wii kal

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

T1 6 12 8 7 6 12 8 7


T3 8 10 7 11 8 10 7 11



10

T5 6 7 8 8 6 7 8 8

Wii kal magi kitoro gi ka acel ka kipoko I oduu ma tino tino. Lapur pe ki kilo me pimo cam mo keken ento tye ki koc ma dite tye lita 0.5 ki bene ngeyo ni pek pa kal tye kg 630/m3. Nyig kal ma ki dino ki ikom oduu acel ma tidi ni opongo koc man tyen ariyo. Nyig cam ma rom kwene ma lapur man twero kayo ki ii poto man ma dite tye ha 1.5 ni?


48

Lim pa Uno How 12 i poto… Byeko dit pa dero cam/citua ma mite –

lapo wic/kwan odoco


49

Kit ma wa neno i lim me 10 – folmila ma pat pat bino mite me tiyo dwonge pa citua ma nukta git ye pat pat nyo cailo


Byeko dit pa dero cam/citua ma mite – lapo wic/kwan odoco

Cura me nongo dwonge pa cailo (lapo wic/kwan odoco).

Cailo pa lyro tye ma obedo cilinda ki wiye ma ki onyo ki lum, kit ma kigoyo cal mere piny kany. En obyeko ni ibininongo kg 2,050 me anyogi ki i poto mere me aketa i citua.

Cilinda man lamale tye mita 2 ka diamita ne tye m 1.5. Fomila me nongo dwonge pa cilinda = π r2 h h = 2 m ka r = 0.75 m (radiac = diamita ÷ 2). 3.142 x 0.752 x 2 = m3 3.53.

Pi man, dwonge pa cailo pa lyro tye m3 3.53

Lapeny me atima pi cawa manok 17 – cura me nongo dwonge pa cailo.



Lamale (h) = m 2

Diamita (d) = m 1.5

Nong dwonge pa cailo magi (cal magi pe kigoyo ma rom ki cac pa cailo magi). 1 2 3

Lamale = m 1 Diamita = m 1.4

Lamale = m 1.5 Radiac = m 0.5

Lamale = m 1.5 Diamita = m 0.6


50

Me nongo pek pa nyig cam ma koc twero tingo (rwom dite) wanyayo dwonge pa koc man ki

bal denciti pa nyig kodi meno.


Byeko dit pa dero cam/citua ma mite – lapo wic/kwan odoco Cura me nongo rwom me gwoko cam pa dero/citua.

Iyro ni itye ki kg 2,050 me anyogi manyige ma en mito gwoko, ka dong cailo ma rwom dite tye m3

3.53. En bimite ni otii ki bal denciti pa anyogi me we ken obyek wel kilo anyogi ma cailo man twero tingo. Bal denciti pa anyogi tye kg 720/m3.

720 x 3.53 = kg 2,542, ma man ki twwro raunding twero piny me doko kg 2,540. Cailo pa lyro twero tingo kg 2,540 me anyogi. En dong pi man myero obed ki kero me piko anyogi mere ducu i cailo man.

Lapeny me atima pi cawa manok 18 – cura me nongo dit pa citua me gwoko cam kun kitiyo ki bal valu me bal denciti values



Kace dwonge pa citua dong ngene, pek pa nyig

cam ma tye idero twero byeke kun kitiyo ki bal

denciti.

1 Lapur tye ki cailo ma obedo ii nukta me cilinda, lamale tye m 1 ka diamita ne tye m 0.7 a) Nong dwonge pa cailo man. b) Byek kabir ma rom kwene (i kg) ma en twero gwoko ii cailo man.

2 Lapur tye ki cailo ma obedo box ma tye I nukta kiuboid ma lamale tye m 1, bore tye m 1 kadong lace tye m 0.5. a) Nong dwonge pa cailo man. b) Byek anyogi ma rom kwene (i kg) ma en twero gwoko ii cailo man.

3 Lapur tye ki cailo ma tye inukta pa cilinda, ma lamale tye m 0.75 ka diamita ma tye m 0.6. a) Nong dwonge pa cailo man. b) En tye ki kg 150 me kal me agwoka. En twero bedo ki kero me gwoko kal magi ducu I cailo eni? 4 Lapur tye ki cailo ma obedo box ma tye inukta pa kiuboid, lamale tye m 2, lace tye m 1.5 ka bore tye m 2.5. a) Nong dwonge pa cailo man. b) Ent ye ki tan 5 me anyogi me agwoka. En twero bedo ki kero me gwoko anyogi magi ducu i cailo eni?


51

Kit ma wa neno con caa, ii lim me 10, hemicpirod obedo nucu pa cipia, ento hemicpirod

obedo cipia ma ki bapo ki man nongo tye ki dite ma pe rom i lacim ma pat pat.

Yoo me nongo dwong pa hemicpirod = 2/3 π x r1 x r2 x r3

Me nongo lamal pa oduu, tep meja kitwero rwako donyo ki I dyer oduu man ka ki neno lamale.

Oduu ma tye ki malo ni cok cok ki hemipirod, kit ma tye ki nucu pa lawala ma cek ki ma mabor ni ki lamale ma tye m 1. Man dok obab loyo hemicpia kit ma nyig cam pe weko kare wek hemicpia oyube ka gin ma jolo tere pe tye. Nen Maber: oduu me nyig cam ma ony ki i cuma tye ma nen calo kon ma dwonge = 1/3 π r2h, ma h = lamal pa kon ka r = radiac pa kon.



Pimo dwonge pa oduu (Kwan adoco).

Himicpirod

Iyro otwoyo, odino ka oonyo kal mere idure. En opimo lamale ka nucu pa lawala aryo, ma cek ki ma bor kun tiyo ki rula.

Dwonge pa nyig cam ma tye I oduu twero nonge

kun nongo itiyo ki yoo me nongo hemicpiroid.


52

Yoo me nongo dwonge pa hemicpirod = 2/3 π r1 (h) x r2 x r3.

Dwonge pa hemicpirod = 2/3 x 3.142 x 0.8 x 1.4 x 0.6 = m3 1.39. Man ki romo keto ne cok cok me doko = m3 1.4.

Dwong me oduu cam pa lyro = m3 1.4. Lapeny me atima pi cawa ma nok 19 – Pimo dwong pa oduu (cal pe ki goyo ma rwate kid it pa jami ma kigoyo ni).



Lamal pa dure man tye = m 0.8

Nucu lawala ma bor pa tere tye arot = m 1.4

Nucu lawala ma cek pa tere tye arot = m 0.6

1 Lapur tye ki oduu kabir. Oduu man tye inukta pa hemicpirod.

r1 = m 0.5 r2 = m 2 r3 = m 0.4

Dwonge pa hemicpirod man tye adii ii m3?

2 Lapur tye ki dero me anyogi. Oduu man ma ocung ki tung wiye ni tye nukta pa hemicpirod.

r = m 1.5

What is the volume of the grain in m3?

3 Lapur tye ki oduu me kabir. Oduu man tye ki nukta pa hemicperod.

r1 = m 0.6 r2 = m 2.1 r3 = m 1.3

Dwonge pa dure man tye adi ii m3?


53

Me byeko pek pa nyig cam ma tye I oduu.

Nyaa dwonge ma mege ki peke.



Byeko pek pa nyig cam ma tye i oduu. Oduu pa kal pa lyro ni kibyeko ni dwongee tye cok cok m3 1.4. Pek pa nyig kal tye kg 630/m3. Pi man, pek pa kal man ducu tye 1.4 m3 x 630 = kg 882. Kal pa lyro ni peke duc tye kg 882 nyo tan 0.88.

Lapeny me atima pi cawa ma nok 20 – Byeko pek pa oduu.



Kun itiyo ki pek pa kal, wa twero byeko pek pa kal

ma lyro mito keto ne I dero.

4 A farmer has a cuboid (box) silo measuring 0.7 m wide, 0.6 m in length and 0.8 m high. His heap of maize grain forms a hemispheroid with r1 = 1 m, r2 = 0.6 m and r3 = 0.25 m. Estimate how much the maize grain weighs. Will the farmer’s maize grain fit in his silo?

4 A farmer has a cuboid (box) silo measuring 0.7 m wide, 0.6 m in length and 0.8 m high. His heap of maize grain forms a hemispheroid with r1 = 1 m, r2 = 0.6 m and r3 = 0.25 m. Estimate how much the maize grain weighs. Will the farmer’s maize grain fit in his silo? Estimate how much the maize grain weighs. Will the farmer’s maize grain fit in his silo?

4 A farmer has a cuboid (box) silo measuring 0.7 m wide, 0.6 m in length and 0.8 m high. His heap of maize grain forms a hemispheroid with r1 = 1 m, r2 = 0.6 m and r3 = 0.25 m.

1 Lapur tye ki oduu me kabir ma dwonge tye m3 2.5. Pek pa kabir man i kilo tye adii?

2 Oduu me kal tye ki dwonge me m3 1.3. Pek pa kal man i kilo tye adii?

3 Oduu me pul manyige tye ki dwonge me cm3 180,000. Pek pa pul man i kilo tye adii?

4 Lapur tye ki dero ma obedo cal ki (bok) ma dite tye 0.7 ii lace, 0.6 m bore ka 0.8 lamale. o me anyogi mere oyubu hemicpirod ma tye ki r1 = 1 m, r2 = 0.6 m ka r3 = 0.25 m. Byek pek pa anyogi man twero bedo kilo adii. Anyogi pa lapur man twero rwate ki cailo

man?.


54



Wel kicaa ma mite.

Tad ka Mim mito gwoko anyogi manyige ma aa ki ikom tunu anyogi ma gin ogwoko ii dero ma megi, ii kicaa. Uno tye ki kg 50 me acata. Me nongo kicaa adii ma gi mito, gin poko pek pa cam ma nyige man ducu ki pek pa nyig cam man ma kicaa acel acel twero tingo, pi man kg 50. Tad ka Mim gitye ki byeka ni gin bino bedo ki kg 1,140 me anyogi ma nyige iyoo nge tinyo tunu anyogi ma megi man. 1,140 ÷ 50 = 22.8 Gi mito kicaa 23.

Lapeny me atima pi cawa manok 21 – Byeko rwom dit pa dero me gwoko cam.(kwan.odoco); gwoko cam ii kicaa

Cam ma nyige gitwero gwoko ne I ki caa ma pat ki

dero bene. Me nongo wel kicaa ma mite, pok pek

pa nyig cam meno ki dit pa kicaa acel.

1 Lapur tye ki cailo ma opong ki tunu anyogi. Dero ma obedo lace ma kipimo dok tye ki: L (Bore) = m 1.5, H (Lamale) = m 1.1, W (Lace) = m 0.8. Lapur opongo koc ma tye lita 20 ki lanyut me tunu 40 ma ducu pek git ye g 2,240. Byek kg adii me anyogi ma nyige ma kitwero nongo ki tunu anyogi magi ma tye I dero. Ka nyig cam ma myero ki gwok ii kicaa ma tero kg 20, Kicaa adii ma lapur man bino mito? Ka kicaa acel acel tye Shs 1.25, cilling adii ma kicaa magi ducu twero tero?

2 Dero pa lapur tye ma opong ki tunu anyogi. Dero man ki twero poko doko lace ma tye ki pirizim ki tung wiye. Man tye pim magi. Kiuboid = L (Bore) = m 2.5, W (Lace)= m 0.9, H (Lamale) = m 1 Pirizim = L(Bore) = m 2.5, B = (Tere) m 0.9, H(Lamale) = m 0.4 Lapur opongo koc ma tye lita 30 ki lanyut 45 me tunu anyogi. Nyig anyogi ma oaa ki ikom tunu 45 magi telo g 3,240. Byek kilo adii me anyogi ma nyige ma twero nonge ki ikom tunu anyogi ma tye ii cailo. Ka cam ma nyige ki gwoko ii kicaa ma tye kg 50, kicaa adii ma lapur man twero bedo kwede? Ka kicaa acel acel tye Shs 2.50, Kicaa ma iye tye nono adii ma cilling man twero wilo?


55

Lapeny me atima pi cawa manok 21 – Byeko rwom dit pa dero me gwoko cam.(kwan.odoco); gwoko cam ii kicaa omede…


Kombedi dong ityeko buk me 3

3 Lapur tye ki cailo ma obedo cilinda dok opong ki wii anyogi, Matye ki kit gi ma tye piny eno: H (Lamale) = m 2; r (radiac) = m 0.5 Lapur opongo koc ma dite tye lita 10 ki lanyut me tunu anyogi 25 me wii kabir. Kabir manyige ma oaa ki iwii kabir 25 caa otelo g 3000. Byek kg adii ma ki twero tinyo dok aa ki iwii kabir magi ma tye ii cailo. Ka cam ma nyige ki gwoko ii kicaa ma tero kg 10, kicaa adii ma lapur myero obed ki miti iye? Ka kicaa acel acel tye Shs 75, Kicaa magi ma yigi nono ni twero tero cilling adii?

4 Cailo pa lapur opong ki tunu anyogi. Cailo obedo kiuboid ma tye ki pim magi: L (Bore) = m 1.2, H (Lamale) = m 0.80, W (Lace) = m 0.80 Lapur okwanyo lanyut me tunu anyogi 48, man opongo koc ma dite tye lita 30. Ka kitinyo, nuig anyogi ma oaa ki ikom tunu magi pongo 1/3 pa koc me lita 30. En pe ki kilo. Kun itiyo ki bal denciti pa anyogi (0.72 kg/l), tii ki ngec man me byeko nyig cam ma rom kwene ma ki twero nongo inge tinyo tunu magi ma tye i citua ni. Ka lapur nongo tye ka gwoko nyig cam ii.kicaa ma tero kg 20, kicaa adii ma en bino mito? Gin ducu bino tero cilling adii ka acel acel tye iwel me Shs 95?


56

Lagam pi Lapeny me atima pi Cawa Manok Lapeny me atima pi cawa manok 1- Kati ki wel kabedo me kwanyo lanyut.

Lagam 1 Lapur twero tic ki 5, ma tero totol me lanyut 20 (lanyut 4 ki kwanyo ki ii acel acel). Labol pa trangcek ma tye ii nukta “W” kinyutu pire piny.

2 Lapur twero tiic ki 3, ma tero totol me lanyut 12 (lanyut 4 ki kwanyo ki ii acel acel). Labol pa trangcek ma lapur twero tic kwede ki nyutu pire piny.

3 Pi poto Marom, lapur twero tic ki 10, kun kwanyo totol me lanyut 40 (capul 4 ma ki kwanyo ki ii acel acel). Ma ben twero bedo ma rom aroma ki poto ma pe tye ma rom. Labol pa trancek ma tye ii nukta “W” kinyutu pire piny.

Lapeny me atima pi cawa manok 2 – Cura me nongo katikati me wel cam ma tye ii m2 acel Lagam

1. Katikati me wel cam ducu pa cam ma tye ka dongo/m2 = 2.55



4. Katikati me wel cam ducu pa cam ma tye ka dongo/m2

= 2.1

Tito kit ma cura man otime kwede 1 Katikati ducu me wel cam ma tye ka dongo/m

2 =2.55

Tecen Namba me wel cam ma tye kadongo

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Katikati me wel cam ma tye ii lanyut acel

T1 5 3 4 2 14 14/4 = 3.5

T2 4 7 4 1 16 16/4 = 4

T3 0 0 0 1 1 1/4 = 0.25

T4 2 3 3 0 8 8/4 = 2

T5 3 2 1 6 12 12/4 = 3

Katikati ducu liweng = 3.5 + 4 + 0.25 + 2 + 3 = 12.75/5 = 2.55

Dok cen (ii lapeny)


57

2 Katikati me wel cam ducu pa cam ma tye ka dongo/m2 = 5.45


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



T1 8 7 5 4 24 24/4 = 6

T2 7 6 4 3 20 20/4 = 5

T3 7 5 8 8 28 28/4 = 7

T4 0 4 6 7 17 17/4 = 4.25

T5 3 4 8 5 20 20/4 = 5 Katikati ducu liweng = 6 + 5 + 7 + 4.25 + 5 = 27.25/5 = 5.45 3 Katikati me wel cam ducu pa cam ma tye ka dongo/m

2 = 2.83


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



T1 4 5 0 1 10 10/4 = 2.5

T2 4 6 1 1 12 12/4 = 3

T3 2 4 6 0 12 12/4 = 3 Katikati ducu liweng = 2.5 + 3 + 3 = 8.5/3 = 2.83 4 Katikati me wel cam ducu pa cam ma tye ka dongo/m

2 = 2.1


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



T1 3 2 1 0 6 6/4= 1.5

T2 4 3 0 1 8 8/4 = 2

T3 5 0 1 2 8 8/4 = 2

T4 4 2 2 2 10 10/4 = 2.5

T5 2 3 1 4 10 10/4 = 2.5

Katikati ducu liweng = 1.5 + 2 + 2 + 2.5 + 2.5 = 10.5 /5 = 2.1

Lapeny me atima pi cawa manok 3 – Cura me nongo wel katikati me tunu anyogi ma tye ii kom tyen anyogi acel Lagam

1. Katikati ducu me wel tunu anyogi ma tye ii tyen anyogi acel acel = 1.78 2. Katikati ducu me wel tunu anyogi ma tye ii tyen anyogi acel acel = 1 3. Katikati ducu me wel tunu anyogi ma tye ii tyen anyogi acel acel = 2

Tito kit ma cura man otime kwede 1 Katikati ducu me wel tunu anyogi ma tye ii tyen anyogi acel acel = 1.78


Lanyut me 1 Lanyut me 2 Lanyut me 3

Lanyut me 4 Wel tunu anyogi ducu ma tye i


Aureg me tunu anyogi ducu pi tyen anyo acel pi acel acel

T1 1 2 0 Cam ma tye kadong pe tye

3 5 3/5 = 0.6

T2 5 0 1 1 7 4 7/4 = 1.75

T3 2 1 3 2 8 2 8/2 = 4

T4 Cam ma tye kadong pe tye

2 1 2 5 6 5/6 = 0.8

T5 4 Cam ma tye kadong pe tye

2 1 7 4 7/4 = 1.75

Katikati ducu = 0.6 + 1.75 + 4 + 0.8 + 1.75 = 8.9/5 = 1.78

Dok cen (ii lapeny)


58

2 Katikati ducu me wel tunu anyogi ma tye ii tyen anyogi acel acel = 1 Tecen Wel tunu anyogi

Lanyut me 1 Lanyut me 2

Lanyut me 3 Lanyut me 4 Wel tunu anyogi ducu ma tye i



T1 2 1 Cam ma tye kadong pe tye

1 4 4 4/4 = 1

T2 1 2 3 1 7 6 7/6 = 1.17

T3 Cam ma tye kadong pe tye

3 0 1 4 5 4/5 = 0.8

T4 2 4 1 Cam ma tye kadong pe tye

7 7 7/7 = 1

T5 3 1 1 2 7 8 7/8 = 0.88

Katikati ducu = 1 + 1.17 + 0.8 + 1 + 0.88 = 4.85/5 = 0.97, ma wa twero raunding doko 1. 3 Katikati ducu me wel tunu anyogi ma tye ii tyen anyogi acel acel = 2


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4




T1 4 4 1 5 14 7 14/7 = 2

T2 4 5 2 1 12 5 12/5 = 2.4

T3 2 3 1 2 8 5 8/5 = 1.6 Katikati ducu = 2 + 2.4 + 1.6 = 6/3 = 2

Lapeny me atima pi cawa manok 4 – Byeko wel tunu anyogi ducu ma tye ii poto

Lagam

1. Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 1.5 = 30,000 2. Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 1 = 39,240 3. Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 1.25 = 15,875 4. Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 0.6 = 11,400

Tito kit ma cura man otime kwede 1 Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 1.5 = 30,000.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1


T1 3 4 0 1 4 2 Cam ma tye kadong pe tye

2

T2 2 5 3 0 2 3 4 Cam ma tye kadong pe tye

T3 1 3 2 1 2 2 2 1

T4 4 0 2 3 5 Cam ma tye kadong pe tye

2 3


3

Meja ma nyen ma tye piny eno nyutu figa ma ononge inge timo cura pa lapeny me 1

Wel cam ducu ma tye ii

Wel tunu anyogi ducu ma tye ii

Katikati me wel cam ma tye/ m

2


T1 8 8 8/4 = 2 8/8 = 1

T2 10 9 10/4 = 2.5 9/10 = 0.9

T3 7 7 7/4 = 1.75 7/7 = 1

T4 9 10 9/4 = 2.25 10/9 = 1.1

T5 6 6 6/4 = 1.5 6/6 = 1

Katikati ducu me cam me tye/ m2 10/5 = 2

Katikati ducu me wel tunu anyogi/cam 5/5 = 1

Dok cen (ii lapeny)


59

Wel katikati me tunu anyogi/m2 = 2 x 1 = 2/m

2 = tunu 20,000 pi ha acel.

20,000 x 1.5 ha = tunu 30,000 ma tye ii poto ma tye ha 1.5.

2 Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 1.5 = 39,240.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Lanyut me 4

T1 2 3 1 2 3 3 2 2

T2 4 1 7 2 5 2 4 3

T3 0 5 6 5 Cam ma tye kadong pe tye

6 4 6

T4 4 7 6 7 6 6 5 7


2 6





2


T1 8 10 8/4 = 2 10/8 = 1.25

T2 14 14 14/4 = 3.5 14/14 = 1

T3 16 16 16/4 = 4 16/16 = 1

T4 24 24 24/4 = 6 24/24 = 1

T5 10 12 10/4 = 2.5 12/10 = 1.2

Katikati ducu me cam me tye/ m2 18/5 = 3.6

Katikati ducu me wel tunu anyogi/cam 5.45/5 = 1.09

Wel katikati me tunu anyogi/m2 = 3.6 x 1.09 = 3.924 = tunu 39,240 ma tye ii poto ma tye ha 1.

3 Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 1.25 =15,875


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Lanyut me 4


3 2 4


1 Cam ma tye kadong pe tye


Cam ma tye kadong pe tye

2 2





2


T1 6 9 6/4 = 1.5 9/6 = 1.5

T2 3 3 3/4 = 0.75 3/3 = 1

T3 3 4 3/4 = 0.75 4/3 = 1.3

Katikati ducu me cam me tye/ m2 3/3 = 1

Katikati ducu me wel tunu anyogi/cam 3.8/3 = 1.27

Wel katikati me tunu anyogi/m2 = 1 x 1.27 = 1.27 = tunu 12,700 pi ha acel.

12,700 x 1.25 = tunu 15,875 ma tye ii poto ma tye ha 1.25.

4 Wel tunu anyogi ducu ma ki byeko pi poto ma dite tye ha 0.6 =11,400


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4




4


4 3 3




60




2


T1 6 9 6/4 = 1.5 9/6 = 1.5

T2 8 10 8/4 = 2 10/8 = 1.25

T3 6 4 6/4 = 1.5 4/6 = 0.67

Katikati ducu me cam me tye/ m2 5/3 = 1.67

Katikati ducu me wel tunu anyogi/cam 3.42/3 = 1.14 Wel katikati me tunu anyogi/m

2 = 1.67 x 1.14 = 1.9 = tunu 19,000 pi ha acel.

19,000 x 0.6 = tunu 11,400 ma tye ii poto ma tye ha 0.6.

Lapeny me atima pi cawa manok 5 – Dwonge pa kiuboid Lagam

1. Dwonge pa kuret = m3 1.6

2. Dwonge pa kuret = m3 0.14

3. Dwonge pa dero = m3 1

4. Dwonge pa dero = m3 2.7

Tito kit ma cura man otime kwede 1 Dwonge pa kuret = m3 1.6 Dwonge = W x H x L = 100 x 100 x 160 = 10,000 x 160 = cm3 1,600,000

cm3 1,000,000 = m3 1 1,600,000/1,000,000 = m3 1.6

Loko wek odok m ma peya icako timo cura ma meri.

W= cm 100 = m 1 H = cm 100 = m 1 L = cm 160 = m 1.6 Dwonge = 1 x 1 x 1.6 = m

3 1.6

2 Dwonge pa kuret = m3 0.14

Dwonge = H x W x L = 0.5 x 0.2 x 1.4 = 0.1 x 1.4 = m3 0.14

3 Dwonge pa dero = m3 1

Dwonge = W x H x L = 0.5 x 1 x 2 = 0.5 x 2 = m3 1

4 Dwonge pa dero = m3 2.7

Dwonge = W x H x L = 0.6 x 1.5 x 3 = 0.9 x 3 = m3 2.7

Lapeny me atima pi cawa manok 6 – Dwonge pa cilinda Lagam

1. Dwonge pa cilo = m3 4.71



4. Dwonge pa koc =, cm3 7,855 = lita 7.86

5. Dwonge pa abino = cm3 1,571 = lita 1.57

Tito kit ma cura man otime kwede 1 Dwonge pa cilo = m3 4.71

Dwonge = π r2 x H = 3.142 x 1

2 x 1.5 = 3.142 x 1 x 1.5 = 3.142 x 1.5 = m

3 4.713

2 Dwonge pa cilo = m3 1.57

Dwonge = π r2 x H = 3.142 x 0.5

2 x 2 = 3.142 x 0.25 x 2 = 3.142 x 0.5 = m

3 1.571

3 Dwonge pa cilo = m

3 1.77

Dwonge = π r2 x H = 3.142 x 0.75

2 x 1 = 3.142 x 0.56 x 1 = 3.142 x 0.56 = m

3 1.767

4 Dwonge pa koc = cm

3 7,855

Dok cen (ii lapeny)

Dok cen (ii lapeny)


61

Dwonge = π r2 x H = 3.142 x 10

2 x 25 = 3.142 x 100 x 25 = 314.2 x 25 = cm

3 (nyo ml ) 7,855 = lita 7.86

5 Dwonge pa abino = cm3 1,571

Nge ni, ii cura man diamita ki miyo ma ka radiac. Pien r= d/2, myero ipok diamita iye ariyo wek inong radiac.

Dwonge = π r2 x H = 3.142 x 5

2 x 20 = 3.142 x 25 x 20 = 3.142 x 500 = cm

3 (nyo ml) 1,571 = lita 1.57.

Lapeny me atima pi cawa manok 7 – Dwonge pa pirizim Lagam

1. Dwonge pa pirizim = m3 0.25

2. Dwonge pa pirizim = m3 1.88


Tito kit ma cura man otime kwede 1 Dwonge pa pirizim = m

3 0.25

Dwonge = ariya pa traengul (a) x bore = ½ x B x H x L = ½ x 0.5 x 0.5 x 2 = ½ x 2 x 0.5 x 0.5 = 1 x 0.5 x 0.5 = 1 x 0.25 = m

3 0.25

2 Dwonge pa pirizim = m3 1.88

Dwonge = a x L = ½ x B x H x L = ½ x 1.5 x 1 x 2.5 = ½ x 1.5 x 2.5 = ½ x 3.75 = m3 1.875

3 Dwonge pa dero = m3 0.86

Dwonge pa pirizim = a x L = ½ x B x H x L = ½ x 0.5 x 0.3 x 1.5 = ½ x 0.15 x 1.5 = ½ x 0.22 = 0.11 Dwonge pa kiuboid = H x W x L = 1 x 0.5 x 1.5 = 0.5 x 1.5 = 0.75 Dwonge ducu = 0.11 + 0.75 = m

3 0.86

Lapeny me atima pi cawa manok 8 – Dwonge pa dure (hip) Lagam

1. Dwonge pa dure = 7.87 m3






Tito kit ma cura man otime kwede 1 Dwonge pa dure (kon) = m

3 7.87

Dwonge pa kon = 1/3 π r2 h

= 1/3 x 3.142 x 2.25

2 x 1.5 = 0.33 x 3.142 x 5.06 x 1.5 = m

3 7.87

2 Dwonge pa dure = m

3 0.39

Dwonge pa hemispirod = 2/3 π x r1 x r2 x r3 = 0.66 x 3.142 x 0.5 x 0.75 x 0.5 = m

3 0.388

3 Dwonge pa kon = m

3 0.26


= 1/3 x 3.142 x 1

2 x 0.25 = 0.33 x 3.142 x 1 x 0.25 = m

3 0.259

4 Dwonge pa kon = m3 0.78


= 1/3 x 3.142 x 1

2 x 0.75 = 0.33 x 3.142 x 1 x 0.75 = m

3 0.777


3 7.25

Dwonge pa hemispirod = 2/3 π x r1 x r2 x r3 = 0.66 x 3.142 x 1.75 x 2 x 1 = 0.66 x 3.142 x 3.5 = m

3 7.25


3 0.51


= 1/3 x 3.142 x 1

2 x 0.5 = 0.33 x 3.142 x 1 x 0.5 = m

3 0.51

Lapeny me atima pi cawa manok 9 – Dwonge pa dero

Lagam 1. Dwonge pa dero = m

3 1.55


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Tito kit ma cura man otime kwede 1 Dwonge pa dero = m

3 1.55

Dwonge pa pirizim = a x L = ½ x B x H x L = ½ x 0.5 x 0.4 x 2.2 = ½ x 0.20 x 2.2 = 0.106 x 2.2 = m3 0.23

Dwonge pa kiuboid = H x W x L = 1.2 x 0.5 x 2.2 = 0.6 x 2.2 = m3 1.32

0.23 + 1.32 = m

3 1.55

2 Dwonge pa dero = m

3 4.2

Dwonge pa pirizim = a x L = ½ x B x H x L = ½ x 0.8 x 1 x 2 = 0.4 x 2 = m3 0.8

Dwonge pa kiuboid = H x W x L = 1.7 x 1 x 2 = 1.7 x 2 = m3 3.4

0.8 + 3.4 = m

3 4.2

Lapeny me atima pi cawa manok 10 – Wel tunu nyo wii anyogi ma tye ii cito. Lagam

1. Lapur tye cok cok ki tunu anyogi 3,600 ii dero ma mere 2. Lapur tye cok cok ki tunu anyogi 4,250 ii dero ma mege 3. Lapur tye cok cok ki wii anyogi 6,000 ii dure ma mere 4. Lapur tye cok cok ki wii anyogi 2,500 ii dero ma mere

Tito kit ma cura man otime kwede 1 Lapur tye cok cok ki tunu anyogi 3,600 ii dero ma mere Tunu anyogi 18 tero dwonge me lita 10 Dero man dite tye m

3 2 man nongo tye 2 x 1,000 lita = lita 2,000 ii dwonge.

Koc ma mite me pongo dero man = 2,000/10 = 200. Ka koc acel tero tunu anyogi 18, man tere ni dero man twero tingo 200 x 18 = tunu 3,600.

2 Lapur tye cok cok ki tunu anyogi 4,250 ii dero ma mere Tunu 34 tero dwonge me lita 20. Dero man dite tye m

3 5 ma tye 5 x 1,000 lita = lita 5,000 ii dwonge

Dero man tye ma opong nucu ne keken, pi man dwonge pa tunu anyogi man tye lita 2,5000 Koc ma mite me pongo dwonge pa tunu anyogi = 2,500/20 = 125. Ka koc acel tero tunu anyogi 34, man tere nucu pa dero man tero 125 x 34 = tunu 4,250 3 Lapur tye cok cok ki wii anyogi 6,000 ii dure ma mere. Wii anyogi 30 tero dwonge me lita 10. Dure opimo m

3 2 ma en aye 2 x 1,000 lita = lita 2,000 ii dwonge

Wel koc ma mite me pongo dero = 2,000/10 = 200. Ka koc acel tingo wii anyogi 30, man tere ni dure man tye ki cok cok 200 x 30 = wii 6,000.

4 Lapur tye cok cok ki wii anyogi 2,500 ii dure ma mere. Wii anyogi 50 tero dwonge me lita 20. Dure opimo m

3 1 ma en aye 1 x 1,000 lita = lita 1000 ii dwonge

Koc ma mite me pongo dero = 1,000/20 = 50. Ka koc acel tero wii anyogi 50, man tere ni dure man tye cok cok ki 50 x 50 = wii anyogi 2,500.

Lapeny me atima pi cawa manok 11 – Byeko pek pa cam ma tye ii citua ni aa ki ii pek pa lanyut Lagam

1. Dero tye ki tunu anyogi cok cok 900, ma twero miyo cook cok kg 36 me anyogi ma nyige

2. Dero tye ki tunu anyogi cok cok 15,000 ma twero miyo cok cok kg 937.5 me anyogi ma nyige

Tito kit ma cura man otime kwede 1 Dero tye ki tunu anyogi cok cok 900, ma twero miyo cook cok kg 36 me anyogi ma nyige Dwonge pa dero tye 1.2 x 1 x 0.5 = m

3 0.6 = lita 600.

Koc adii ducu ma twero pongo dero man? 600/10 = 60. Ka koc acel tero tunu 15, man tere ni dero ma mere ni tero 60 x 15 = tunu 900

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Anyogi manyige ma aa ki ii koc acel telo kg 0.6 Pi man, dero man tero cok cok ki 60 x 0.6 = kg 36 me anyogi ma nyige. 2 Dero tye ki tunu anyogi cok cok 15,000 ma twero miyo cok cok kg 937.5 me anyogi ma nyige Dwonge pa pirizim tye ½ x 1 x 1 x 3 = m

3 1.5.

Dwonge pa kiuboid tye 2 x 3 x 1 = m3 6.

Pi man, dwonge pa kiuboid ducu = 1.5 + 6 = 7.5 m3 ma rom aroma ki lita 7500.

Tero koc adii wek dero man opong? 7,500/20 = 375. Ka koc acel tero tunu anyogi 40, man tere ni dero man tero 375 x 40 = tunu 15,000 Pek pa nyig anyogi ma oaa ki ii koc acel telo kg 2.5. Pi man, dero man tero cok cok 375 x 2.5 = kg 937.5 me anyogi ma nyige.

Lapeny me atima pi cawa manok 12 – Cura me nongopek pa cam pa tye ii citua kun watiyo ki valu pa bal denciti Lagam

1. Dero tye ki tunu anyogi ma cok cok 448, ma twero miyo cok cok kg 46 me anyogi manyige. 2. Dure tye ki cok cok kg 1,590 me pul ma golo.

3. Dero tye ki cok cok kg 183 me nyig cam

Tito kit ma cura man otime kwede 1 Dero tye ki tunu anyogi ma cok cok 448, ma twero miyo cok cok kg 46 me anyogi manyige. Dwonge pa dero = 1 x 0.8 x 0.4 = m

3 0.32 ma rom ki lita 320

Wel koc ma mite me pongo dero = 320/20 = 16. Ka koc acel tero tunu 28, man tere ni dero tero 28 x 16 = tunu 448 Nyig anyogi ma oaa ki ikom tunu 28 opongo acel me abic pa koc ma dite tye lita 20 ma tye cok cok ki 1/5 x 20 = lita 4 Bal denciti pa anyogi ma nyige tye kg 0.72/lita Pi man, lita 4 me anyogi ma nyige telo cok cok 4 x 0.72 = kg 2.88 Pi meno dero dong tero cok cok ki 16 x 2.88 = kg 46 pa anyogi ma nyige. 2 Dure tye cok cok ki kg 1,590 me pul ma golo Dwonge pa dure = 2/3 x π x 1.6 x 0.8 x 2 = 0.66 x 3.142 x 1.6 x 0.8 x 2 = m

3 5.3 ma rom ki lita 5,300.

Bal denciti pa pul ma golo tye kg 0.30/lita Pe ma, dero man tye cok cok ki 5,300 x 0.3 = kg 1,590 pa pul ma golo. 3 Dero tye cok cok ki kg 180 me kabir ma nyige. Vaum pa crib = m

3 2.5 ma rom ki lita 2,500

Wel koc ma mite me pongo dero man tye = 2,500/25 = 100. Nyig cam ma oaa ki ii lita 25 me wi anyig cam opongo koc me lita 5 ma nongo tye 1/2 x 5 = lita 2.5 Bal denciti pa kabir tye kg 0.73/lita Pi man, nyig cam ma oaa ki ii koc me lita 25 me wii cam otelo cok cok 2.5 x 0.73 = 1.83 kg. Pi man dero man tye cok cok ki 100 x 1.83 = kg 183 pi cam ma nyige.

Lapeny me atima pi cawa manok 13 – Katikati me wel tunu nyo wii cam/m2

Lagam 1. Byeka me wel tunu anyogi ma tye ii poto =32,700 2. Byeka me wel wii cam ma tye ii poto = 16,850 3. Byeka me wel wii cam ma tye ii poto = 102,000

Tito kit ma cura man otime kwede 1 Byeka me wel tunu anyogi ma tye ii poto =32,700

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64


Wel tunu anyogi

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Lanyut me 4

T1 1 3 2 3 1 3 4 5



5 4 4


3 5


6 5 3

Wel cam ducu ma tye ka dongo ii

Wel tunu ducu ma tye ii

Katikati me wel cam ducu ma tye / m

2

Katikati me wel tunu ma tye pi tye cam acel

T1 9 13 9/4 = 2.25 13/9 = 1.44

T2 8 12 8/4 = 2 12/8 = 1.5

T3 9 13 9/4 = 2.25 13/9 = 1.44

T4 11 13 11/4 =2.75 13/11 = 1.18

T5 9 14 9/4 = 2.25 14/9 = 1.55

Katikati ducu me cam ma tye ka dongo /m

2 = 2.25 + 2 + 2.25 + 2.75 + 2.25 = 11.5/5 = 2.3

Katikati ducu me wel tunu anyogi ma tye ii tyen cam acel = 1.44 + 1.5 + 1.44 + 1.18 + 1.55 = 7.11/5 = 1.42

Katikati me wel tunu/m2 = 2.3 x 1.42 = 3.27

Pi man, ii ha 1 wa byeka wa bi bedo 10,000 x 3.27 = tunu 32,700. 2 Byeka me wel wii cam ma tye ii poto = 16,850

Tecen Wel cam ma tye ka dongo (tyen anyogi) Wel wii

Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1 Lanyut me 2 Lanyut me 3 Lanyut me 4

T1 6 2 4 5 6 2 3 5

T2 8 5 6 3 7 4 6 3


2 4


3


1 5 2




2


T1 17 16 17/4 = 4.25 16/17 = 0.94

T2 22 20 22/4 =5.5 20/22 = 0.91

T3 10 10 10/4 = 2.5 10/10 = 1

T4 13 13 13/4 = 3.25 13/13 = 1

T5 9 8 9/4 = 2.25 8/9 = 0.89


2 = 4.25 + 5.5 + 2.5 + 3.25 + 2.25 = 17.75/5 = 3.55

Katikati ducu me wel wii cam ma tye ii tyen cam acel = 0.94 + 0.91 + 1 + 1 + 0.89 = 4.74/5 = 0.95 Katikati me wel wii cam pi m2 acel = 3.55 x 0.95 = 3.37 ma rom ki 33,700 pi ha acel. Pi man, ii poto ma tye ha 0.5 bi bedo ki wii cam 16,850


65

3 Wii cam ma ki byeko pire ii poto = 102,000


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4

Lanyut me 1 Lanyut me 2 Lanyut me 3 Lanyut me 4


16


9 12

T3 14 16 15 9 14 16 15 9


8 14 18


13 9




2


T1 45 45 45/4 = 11.25 1

T2 31 31 31/4 = 7.75 1

T3 54 54 54/4 = 13.5 1

T4 40 40 40/4 = 10 1

T5 34 34 34/4 = 8.5 1

Katikati ducu pa cam ma tye ii m

2 = 11.25 + 7.75 + 13.5 + 10 + 8.5 = 51/5 = 10.2

Katikati ducu me wii cam ma tye ii m2 acel = 1 + 1 + 1 + 1 + 1 = 5/5 = 1

Katikati me wii cam pi m

2 acel = 10.2 x 1 = 10.2 ma rom ki 102,000 pi ha acel.

Lapeny me atima pi cawa manok 14 – Pek pa nyig cam ma oaa ki ikom tunu acel nyo wii cam acel Lagam

1. Byeka me nyig cam ma aa ki iwi cam acel = g 54 2. Byeka me nyig cam ma aa ki iwi cam acel = g 15 3. Byeka me nyig cam ma aa ki iwi cam acel = g 45 4. Byeka me nyig cam ma aa ki iwi cam acel = g 58 5. Byeka me nyig cam ma aa ki iwi cam acel = g 9.9 6. Byeka me nyig cam ma aa ki iwi cam acel = g 20

Tito kit ma cura man otime kwede 1 Nyig cam ma oaa ki iwii cam 50 otelo kg 2.7. Pi man, nyig cam ma aa ki iwii cam acel telo cok cok 2.7/50 = kg 0.054. 1000 g = kg 1, tere ni nyig cam ma oaa ki iwii cam acel byeka tye ni telo g 54.

2 Tic ki valu pa bal denciti, lita 1 me kal byeka tye ni telo kg 0.63. Lita 0.5 me nyig kal pi man telo 0.63/2 = kg 0.315 ma rom ki g 315. Ka wii cam 21 kelo g 315 me nyig cam, wii cam 1 miyo ki wan 315/21 = g 15 me nyig cam. 3 Tic ki bal denciti ma mere, lita acel me anyogi byek tye ni telo kg 0.72. Lita 2.5 me anyogi pi man telo2.5 x 0.72 = kg 1.8 nyo g 1,800. Ka tunu anyogi 40 kelo cok cok g 1,800 me nyig cam, tunu 1 bi kelo 1,800/40 = g 45 me nyig cam. 4 Tic ki valu pa bal denciti ma mere, lita 1 byek tye ni telo kg 0.72. Nyig cam ma oaa ki ikom lanyut me anyogi opongo koc ma dite tye ml 3 x 400 = ml 1,200 ma rom ki 1,200/1,000 = lita 1.2. Lita 1.2 me anyogi ma nyige telo 1.2 x 0.72 = kg 0.864 nyo g 864. Ka tunu 15 telo cok cok ki g 864 me nyig cam, tunu 1 bino telo 864/15 = g 58 me nyig cam. 5 Tic ki valu pa bal demciti, lita 1 me nyig kal telo cok cok ki kg 0.63. Lanyut me nyig kal opongo lita 1, tyen 1.25 = lita 1.25. Lita 1.25 me nyig kal pi man telo .25 x 0.63 = kg 0.788 nyo g 788. Kaw ii cam 80 kelo cok cok ki g 788 me nyig cam, wii cam 1 bino kelo 788/80 = g 9.85 me nyig cam. 6 Tic ki valu pa bal denciti, lita 1 me kabir telo cok cok ki kg 0.73.

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Nyig kabir ma oaa ki ii lanyut opongo lita 0.5 tyen 6.5 = lita 3.25. Lita 3.25 me nyig kabir pi meno telo 3.25 x 0.73 = kg 2.37 nyo g 2,370. Ka wii cam 120 kelo cok cok ki g 2,370 me nyig cam, wii cam 1 bino kelo 2,370/120 = g 19.8 me nyig cam.

Lapeny me atima pi cawa manok 15 – Nyig cam ma tye ii m2

Lagam

1. g/m2 360

2. g/m2 90 ma rom ki 0.09 kg/m

2

3. g/m2 1.16

Tito kit ma cura man otime kwede 1 Nyig cam ma oaa ki ikom tunu 40 telo g 3,600. Pi man, nyig cam ma oaa ki ikom tunu acel telo 3,600/40 = g 90. Poto tye ki katikati me tunu anyog 4 /m

2.

Byeka me pek pa nyig cam pi m2 acel = 90 x 4 = g/m

2 360.

2 Nyig cam ma oaa ki iwic 17 telo g 510. Pi man, nyig cam ma aa ki iwii cam acel telo 510/17 = g 30. Poto tye ki katikati me wii cam 3 /m

2.

Byeka me pek pa nyig cam pi m2 acel = 30 x 3 = 90 g/m

2 nyo kg 0.09/m

2.

3 Nyig cam ma oaa ki itunu 62 pongo koc ma tye lita 25. Tic ki valu pa bal denciti, man telo cok cok ki 25 x 0.72 = kg 18. Pi man, nyig cam ma oa ki ikom tunu acel telo cok cok ki 18/62 = kg 0.29. Poto tye ki katikati me tunu 4 /m

2.

Byeka me pek pa nyig cam pi m2 acel = 0.29 x 4 = kg 1.16 /m

2.

Lapeny me atima pi cawa manok 16 – Pek pa nyig cam ma tye ii poto Lagam

1. Byeka me cek pa cam ni aa ki ii ha 1 ma mere tye kg 2,003 2. Byeka me cek pa cam ni aa ki ii ha 1.5 ma mere tye kg 1,877

Tito kit ma cura man otime kwede 1 Byeka me cek pa nyig cam ducu tye kg 2,003 me aa ki ipoto mere ma tye ha 1.


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4


Lanyut me 4

T1 5 4 6 3 4 5 5 4


4 5 3


3 2

T4 2 3 3 1 2 4 4 2


5 2




2


T1 18 18 18/4= 4.5 18/18=1

T2 9 12 9/4= 2.25 12/9=1.33

T3 8 8 8/4=2 8/8=1

T4 9 12 9/4= 2.25 12/9=1.33

T5 9 9 9/4=2.25 9/9=1

Katikati ducu pa cam ma tye kadongo ii m

2 acel = 4.5 + 2.25 + 2 + 2.25 + 2.25 = 13.25/5 = 2.65

Katikati ducu me wel tunu anyogi ma tye ka dong pi tyen cam acel acel = 1 + 1.33 + 1 + 1.33 + 1 = 5.66/5 = 1.13 Katikati ducu pa tunu ma tye pi m2 = 2.65 x 1.13 = 2.99 ma rom ki 29,900 pi ha acel.

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Nyig cam ma oaa ki ikom tunu 15 otelo g 1,000. Pi man, nyig cam ma oaa ki ii kom tunu acel telo cok cok ki 1,000/15 = 67 g nyo kg 0.067. Pi man byeka me cek pa cam ducu tye 0.067 kg x 29,900 = kg 2,003 ki ipoto ma mere ha 1. 2 Byeka me cek pa cam tye kg 1,877 ma oaa ki ipoto mere ma tye ha 1.5


Lanyut me 1

Lanyut me 2

Lanyut me 3

Lanyut me 4



T1 6 12 8 7 6 12 8 7


T3 8 10 7 11 8 10 7 11


9 Cam ma tye kadong pe tye

10

T5 6 7 8 8 6 7 8 8




2


T1 33 33 33/4 = 8.25 33/33 = 1

T2 26 26 26/4 = 6.5 26/26 = 1

T3 36 36 36/4 = 9 36/36 = 1

T4 19 19 19/4 = 4.75 19/19 = 1

T5 29 29 29/4 = 7.25 29/29 = 1 Katikati pa cam ma tye ii m

2 acel = 8.25 + 6.5 + 9 + 4.75 + 7.25 = 35.75/5 = 7.15

Katikati ducu pa wii cam ma tye ii tyen cam acel acel = 1 + 1 + 1 + 1 + 1 = 5/5 = 1 Katikati me wii cam ma tye ii m

2 acel = 7.15 x 1 = 7.15 ma rom ki 71,500 pi ha acel.

Pi ha 1.5, man aye wi cam 1.5 x 71,500 = 107,250. Nyig cam ma oaa ki iwii cam 36 pongo koc ma tye lita 2 x 0.5 = lita 1. Nyig kal ki byeko me telo kg 630 /m

3 nyo kg 0.63 /lita.

Kg 0.63 = g 630, pi man, nyig cam ma oaa ki iwii cam acel telo cok cok 630/36 = g 17.5 nyo kg 0.0175. Byeka me cek pa cam ducu pi man dong tye kg 0.0175 x wii cam 107,250 = kg 1,877 ni aa ki ipoto mere ma tye ha 1.5

Lapeny me atima pi cawa manok 17 - Cura me nongo dwonge pa cilo Lagam

1. Dwonge = m3 1.54

2. Dwonge = m3 1.18

3. Dwonge = m3 0.42

Tito kit ma cura man otime kwede 1 Cilinda lamale tye m 1 ka diamita me m 1.4 Fomila me nongo dwonge pa cilinda = π r

2 h

h = m 1 ka r = m 0.7 (wii opoo ni radiac tye nucu pa diamita) 3.142 x 0.7

2 x 1 = m

3 1.54.

2 Cilinda lamale tye m 1.5 ka radiac me m 0.5 Fomila me nongo dwonge pa cilinda = π r

2 h

h = m 1.5 ka r = m 0.5 3.142 x 0.5

2 x 1.5 = m

3 1.18.

3 Cilinda tye ki lamale ma tye m 1.5 ka diamita ma tye m 0.6 Fomila me nongo dwonge pa cilinda = π r

2 h

h = m 1.5 ka r = m 0.3 (Wii opo ni radiac tye nucu pa diamita) 3.142 x 0.3

2 x 1.5 = m

3 0.42.

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Lapeny me atima pi cawa manok 18 – Cura me nongo kero pa cilo me gwoko cam kun watiyo ki bal denciti. Lagam

1. Dwonge me m3 0.38, tingo cok cok kg 277 me nyig kabir

2. Dwonge me m3 0.5, tingo cok cok kg 360 me nyig anyogi

3. Dwonge me m3 0.21, tingo cok cok kg 132 me nyig kal = tidi tutwal

4. Dwonge me m3 7.5, tingo cok cok MT 5.4 me nyig anyogi = dit tutwal

Tito kit ma cura man otime kwede 1 Cilinda lamale tye mita 1 ka diamita ma tye mita 0.7 Fomila me nongo dwonge pa cilinda = π r

2 h.

h = m 1 nyo r = m 0.35 3.142 x 0.35

2 x 1 = m

3 0.38

Valu pa bal denciti me kabir tye kg 730/ m3

Pi man, Cilo man bino gwoko cok cok ki 730 x 0.38 = kg 277 me nyig babir. 2 Kiuboid tye ki lamale ma tye m 1, bore m 1 ka lace tye m 0.5 Dwonge = H x L x W = 1 x 1 x 0.5 = m

3 0.5

Bal denciti pa anyogi tye kg 720/m3

Pi man, cilo bino gwoko cok cok ki 720 x 0.5 = kg 360 me nyig anyogi.

3 Cilindatye ki lamale ma tye m 0.75 ka diamita ma tye m 0.6 Fomila me nongo dwonge pa cilinda = π r

2 h

h = m 0.75 ka r = m 0.3 3.142 x 0.3

2 x 0.75 = m

3 0.21

Valu pa bal denciti pa kal tye kg 630/m3

Pi man, cilo man bino gwoko cok cok ki 630 x 0.21 = kg 132 me nyig kal. Pi man, cilo pe bino romo gwoko kg 150 dudu me nyig kal.

4 Cilo tye ki lamale ma tye m 2, bore ma tye m 2.5 ka lace ma tye m 1.5 Dwonge = H x L x W = 2 x 1.5 x 2.5 = m

3 7.5.

Valu pa bal denciti me anyogi tye kg 720/m3.

Pi man, cilo bino gwoko cok cok ki 720 x 7.5 = kg 5,400 me nyig anyogi, ma rom ki 5,400/1,000 = MT 5.4 Pi man, cilo myero obed ma oromo me gwoko MT 5 me nyig cam man.

Lapeny me atima pi cawa manok 19 – Pimo dwonge pa dure (hip) Lagam

1. Volume = m3 0.83

2. Volume = m3 7

3. Volume = m3 3.40

Tito kit ma cura man otime kwede 1 Fomila me nongo dwonge pa hemicpirod = 2/3 π x r1 x

r2 x r3

Dwonge pa dure ma obedo hemicpirod = 2/3 x 3.142 x 0.5 x 2 x 0.4 = 0.66 x 3.124 x 0.5 x 2 x 0.4 = m3 0.83.

2 Fomila me nongo dwonge pa hemicpirod = 2/3 π r3

Dwonge pa dure ma obedo hemicpirod = 2/3 x 3.142 x 1.53 = 0.66 x 3.142 x 1.5 x 1.5 x 1.5 = m

3 7.

3 Fomila me nongo dwonge pa hemicpirod = 2/3 π x r1 x

r2 x r3

Dwonge pa dure ma obedo hemicpirod = 2/3 x 3.142 x 0.6 x 2.1 x 1.3 = 0.66 x 3.142 x 0.6 x 2.1 x 1.3 = m

3 3.40.

Lapeny me atima pi cawa manok 20 – Byeko pek pa dure Lagam

1. Byeka me pek pa dure ducu = kg 1,825 nyo taan 1.825 2. Byeka me pek pa dure ducu = kg 819

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69

3. Byeka me pek pa dure ducu = kg 115

4. Dwonge pa cilo = m3

0.34; Dwonge pa dure = m3 0.31, man bino rwate.

Byeka me pek pa dure ducu = kg 223

Tito kit ma cura man otime kwede 1 Bal denciti pa nyig kabir ma rwome rwate tye kg 730/m

3. Dwonge pa dure tye m

3 2.5.

Pi man, pek pa dure ducu bino bedo cok cok 2.5 x 730 = kg 1,825 nyo taan 1.825.

2 Bal denciti pa nyig kal ma rwome rwate tye kg 630/ m

3. Dwonge pa dure bino bedo cok cok ki m

3 1.3.

Pi man, pek pa dure ducu bino bedo cok cok ki 1.3 x 630 = kg 819. 3 Bal denciti pa pul ma nyige ma rwome rwate tye kg 640/ m

3. Dwonge pa dure tye cm

3 180,000.

cm3 180,000 ki loko ii to m

3 = 180,000/1,000,000 = m

3 0.18

Pi man, pek pa dure ducu bino bedo cok cok ki 0.18 x 640 = kg 115. 4 Dwonge pa cilo ma tye kiuboid = 0.7 x 0.6 x 0.8 = m

3 0.34.

Dwonge pa dure ma obedo hemicpirod =2/3 x π x r1 x r2 x r3 = 0.66 x 3.142 x 1 x 0.6 x 0.25 = m3 0.31

Pi man, nyig cam myero orwate ii cilo man. Bal denciti pa nyig anyogi ma rwome rwate tye kg 720/m

3

Pi man pek pa nyig cam ma tye ii dure bino bedo cok cok ki 0.31 x 720 = kg 223.

Lapeny me atima pi cawa manok 21 – Byeko kero pa cilo me gwoko cam (kwan odoco); gwoko cam ii kicaa sacks Lagam

1. Pek pa nyig cam = kg 147.84. En bino mito kicaa 8, ma bino mito Shs 10 2. Pek pa nyig cam = kg 291.6. En bino mito kicaa 6, ma bino mito Shs 15 3. Pek pa nyig cam = kg 47.1. En bino mito kicaa 5, ma bino mito Shs 3.75 4. Pek pa nyig cam = kg 184.32. En bino mito kicaa 5, ma bino mito Shs 9.50

Tito kit ma cura man otime kwede 1 Dwonge pa cilo = L x H x W = 1.5 x 1.1 x 0.8 = m

3 1.32.

Me loko ii lita: m3 1.32 x 1,000 = lita 1,320.

Dwonge pa koc tye lita 20. Pi man, cilo tye tyen 1,320/20 = 66 dit loyo koc man. Lanyut me koc ma dite tye lita 20 otero g 2,240 me nyig cam (nyo kg 2.24). Pi man, watwero byeko ni cilo man tero 66 x 2.24 kg = kg 147.84 me nyig cam. Man watwero raunding me bedo kg 148. Ka lapur tye ka gwoko nyig cam ii kicaa me kg 20, en bino mito. 148/20 = Kicaa 7.4, ma wa twero raunding doko kicaa 8. Kicaa 8 iwel me Shs1.25 ikom acel 8 x 1.25 = Shs10. 2 Dwonge pa cilo (bute tye kiuboid) = L x W x H = 2.5 x 0.9 x 1 = m

3 2.25.

Dwonge pa cilo (bute tye pirizim) = ½ x L x B x H = ½ x 2.5 x 0.9 x 0.4 = m3 0.45.

Pi man, wel dwonge ducu pa cilo tye 2.25 + 0.45 = m3 2.7.

Lok me doko lita: m3 2.7 x 1,000 = lita 2,700.

Dwonge pa koc tye lita 30 ki man cilo bedo tyen 2,700 /30 = 90 dit loyo koc meno. Lanyut ki koc ma tye lita 30 okelo g 3,240 (nyo kg 3,240). Pi meno, watwero byeko ni cilo tye ki kg 90 x 3.24 = kg 291.6. Man watwero raunding me doko kg 292. Ka lapur tye ka gwoko nyig cam ii kicaa ma tero kg 50, en bino mito: 292/50 = kicaa 5.8, ma wa raunding doko kicaa 6. Kicaa 6 iwel me Shs 2.50 ikom acel kelo 6 x 2.50 = Shs 15. 3 Dwonge pa cilo ma tye cilinda = π r

2 x H

3.142 x 0.5 x 0.5 x 2 = m3 1.57

m

3 1.57 x 1,000 = lita 1,570.

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Dwonge pa koc tye lita 10 pi meno cilo tye tyen 1,570/10 = 157 dit loyo koc man. Lanyut me koc ma dite tye lita 10 okelo g 300 me nyig cam (nyo kg 0.3). Pi man, watwero byeko ni cilo tye ki kg 157 x 0.3 = kg 47.1 me nyig cam. Ka lapur tye ka gwoko nyig cam mere ii kicaa ma tero kg 10, en bino mito: 47.1/10 = kicaa 4.7 ma watwero raunding doko kicaa 5. Kicaa 5 iwel me c 75 ikom acel 5 x 75 = Shs 3.75. 4 Dwonge pa cilo = L x H x W = 1.2 x 0.8 x 0.8 = m

3 0.768

m3 0.768 x 1,000 = lita 768.

Dwonge pa koc tye lita 20 ka dong pi meno cilo tye tyen 768/30 = tyen 25.6 dit loyo koc man. Lanyut me tunu 48 opong acel me adek pa koc ma dite tye lita 30, 1/3 x 30 = lita 10. Bal pike pa nyig anyogi tye kg 0.72/l. Pi man, lanyut pa nyig anyogi man kelo kg 10 x 0.72 = kg 7.2 me anyogi ma nyige. Pi man, watwero byeko ni kg 25.6 x 7.2 = kg 184.32 me nyig cam ki twero nongo ki ii kom tunu ma ki gwoko ii cilo man. Ka la pur tye ka gwoko cam mere ii kicaa ma tero kg 20, en bino mito: 184.3/20 = kicaa 9.2, ma wa raunding doko kicaa 10 Kicaa 10 kom acel tye Shs 95; 10 x 95 = Shs 9.50

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