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KENDRIYA VIDYALAYA SANGATHAN

CCT TEST ITEMS

CLASS IX: CHAPTER 13:SURFACE AREA AND VOLUME

S. No. TITLE OF TEST ITEM1. Pencil Box2. Party Cake3. Packers and Movers4. Painting of House5. Square Watermelon6. Right Choice7. Art Fest8. Ice Cream9. Capsule10. Beautiful Souvenir11. Toddlers Playing with Building Blocks12. Balls in Tanks13. Hemi-Spherical Tank14. Hemispherical Cup15. Metal Balls16. Basketball Match17. Globe18. Painting Competition19. Animal Farm20. Prayer Center21. Toy Maker22. Orange Juice23. Sphere Model24. Birth Day Party25. Coffee Maker26. Sand Clock27. Lemonade Stand28. Aquarium29. Cubical Jars30. Birthday Party31. Palace32. Milkmen33. Tomato Plants34. Coffee Maker35. Swimming Pool36. Garden Hose37. Transport of Crude Oil38. Sand at Building Site39. Wheat Cone40. Pancake Contest41. Making of Battery42. Iron Pipes43. Trash Can44. Grain Silo

45. Class Candles46. Hay Bales47. Thirsty Crow48. Thirsty Cow49. Choco Rolls50. Protein Food

PISA Practice Items Class IX MathematicsSurface areas and Volumes

Item 1(1.1)

Domain: Mathematics literacy Theme:Surface Areas and Volumes

Class: IXExpected time: 5 Min.Total credit: 02

Description of Item

TextImageTableGraphMap Poem

Learning outcome: (as per NCERT) .

Understand and apply surface area

Jamuna a student of eighth standard wanted to make aecho friendly pencil box using a old cardboard. On searching, she got a cardboard of sides 12 inches by 8 inches. She cut out four squares of 2 inches size at corners and folded up the sides to make an open box. She painted it beautifully with blue in the entire interior of the box and the outer with grey and put all her pencils in that.

1.1 ) Find the surface area of the box painted blue.

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea Space and ShapeContext PersonalItem Format Short response itemCognitive process Problem solving.Proficiency Level 2

Credit pattern :Full credit:02Partial credit:01No credit:00

Description of Answer Key and Credits

1.1).Full credit: 02Surface area of the box painted blue= 2h(l+b)+lb =2X2(8+4)+8X4=80 sq.inchesPartial credit: 01If the length and breadth is correct.N.C: Any other response

Name of the Teacher/Item Writer: ARI KUMAR.BDesignation: TGT(MATHS)Email: [email protected] No: 9488080011Name of the vidyalaya: K.V.No-1, Narimedu ,MaduraiKVS Region: Chennai

Item 2(2.1)



Description of Item




A new bakery offers well decorated sheet cakes for parties and other occasions with nicely anti viral lamination. The bakery wants the volume of a small cake to be 351 cubic inches. The cake is to be in the shape of a rectangular solid. The length of the cake is 4 inches longer than the width and height of the cake is 1/3rd of the width and the width of the cake was 9 inches. They have transparent sheets of size 20 inchesX20 inches for lamination.

2.1) What will be the total surface area of the cake prepared?

2.2) Is the transparent sheet available be sufficient for the lamination of the cake?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea SPACE AND SHAPEContext OccupationalItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 3




2.1). Full credit: 02Surface area of the cake = 2(lb+bh+hl) =2(13X9+9X3+3X13)=366 sq.inches

Partial credit: 01If the length, height is calculated correctly.

No Credit: Any other response.2.2). Full credit : 02

YesPartial credit : 1

Area of the sheet calculated.

No Credit : Any other Responses.

Item 3(3.1)



Description of Item




WOODPAG is one of the leading companies in package movers. They are well known for their safe movement of the goods from anywhere to anywhere within the country. There was a great demand for them for this. While packing the goods, they take at most care for the safety so that the goods don’t get damaged. Once during such a packaging, some things were kept inside a cubical container (carton box).Then tape of 12m length was applied all along its edges. And then the box was covered completely with cloth. This packing perfectly ensures the safety of the packed items during its movement to the destination and delivery.

3.1.Find how many square metres of packing cloth would be required for the packing 12 such carton boxes .

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea SPACE AND SHAPEContext OccupationalItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 2



3.1). Full credit: 02Length of one edge=12/12=1m

Surface area of 1 box = 6a2sq.metres, surface area of 12 boxes is 12X6=72 sq.metres

Partial credit: 01

If the length of side of the square is calculated correct.

No Credit : Other responses or no attempt.


Item 4(4.1)



Description of Item




In general, the average cost to paint a house interior is around $1.50 per sq. ft., depending on many factors. The cost to paint the interior of a 1,500 sq.ft home will cost about $1,500–$2,400. For an average home of 2,500 sqft, costs range from $2,100–$3,900+ as reported by Home Guide members. Mr. Kakset wanted to paint his house which is of 1500 sq.ft . He employed two painters a day for two days. He paid the highest wage of $2,400 for that.

4.1) On completion of the work, how much did each painter receive if all of them shared equally?

4.2) What will be the cost of painting four walls of a hall having dimensions

42 ft X 20 ft X 10 ft at the lowest rate of $10 per square ft?

4.3) The outer walls of the entire house of dimension 60ft x 40 ft X 12ft is painted outside leaving a door of size 8ft x 3.5 ft and two windows each of size 3ft X 4ft.Then what area of the outer walls of the house is painted?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea SPACE AND SHAPEContext PersonalItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 2



https://myphotohunter.com/s/?q=house

4.1) Full credit: 02$ 600 eachPartial credit: 01600 (No unit)No Credit: 00Any other responses

4.2) Full credit: 02$ 12400 or 12400Partial credit: 01For correct formulaNo Credit: 00Any other responses

4.3) Full credit: 022348 sq ft Partial credit: 01Finding the area of the wall 2400 sq ft and area of a door 28sq ft., area of window 12 sq.ft eachNo Credit: 00Any other responses


Item 5(5.1)



Description of Item



Understand and apply the concept of surface area

Square watermelons are novel, but also costly and labor-intensive Since the dawn of time, there has been an unspoken rule: When nature is inconvenient, humanity will try to alter nature.From man-made lakes to super-sizing animals, this practice has taken many different forms over the decades. Sometimes for convenience and sometimes for pure entertainment, novelty nature has been spreading more and more to food. It was done not through crossbreeding or genetic modification but with a square-shaped cubical mould.In their natural form, Everything has its price and with the watermelon, the cost of the square shape would be its taste. As a result of being grown in a square mould, the watermelons are unable to reach full maturity. So the not-quite-ripe watermelons do not taste quite as sweet, which is why for some consumers the fruit serves a purely decorative purpose. And speaking of price, square watermelons cost a pretty penny, going anywhere from $75 to $100 per melon.The melons made headlines in the U.S. when they made their way to New York City in 2010.

5.1) If a cubical watermelon measures 60cm X 60 cm X 60 cm, how many square meters of covering paper would be required to completely cover it?

5.2) A cubical part of melon of size 20cm X 20cm X 20cm is removed from a corner of a such melon. After the removal of this part, what will be the ratio of the surface area of the water melon (before the removal of the part) to the remaining part of the melon (after removal of the part).

5.3)A larger melon is divided in to 4 equal small cubes for sale. What would be the total surface area of one of the small cubical melons piece?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea SPACE AND SHAPE

https://myphotohunter.com/s/?q=New%20York%20City

Context SocialItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 2


Description of Answer Key and Credits5.1) Full credit: 02

21,600 sq.cm or 2.16 sq.mPartial credit: 0121600 (No unit)

No Credit: 00Any other responses

5.2) Full credit: 021:1Partial credit: 01For surface area formula of a cube.


5.3) Full credit: 025400 sq.cm or 0.54 sq.mPartial credit: 015400 (No unit)


Item 6(6.1)



Description of Item



Understand and apply the concept of surface area

Select Your Right Device

Picking the right laptop screen size and figuring out how to measure a laptop may sound simple, but it can sometimes be a little more complicated than you think. Are you wondering, “What is my laptop screen size and how do I measure it?” When you’re measuring or comparing screen sizes, remember that almost all display sizes are measured on the diagonal.There is no universal standard when it comes to the display size or overall physical configuration of laptops, On the other hand, the size of displays is a little more consistent, with the majority of laptops featuring between 15-inch and 17-inch displays. Compact laptops tend to range from 11 inches to 14 inches. Having said that, display screen size can still be tricky. Just because two displays have the same diagonal measurement doesn’t mean they have the same vertical and horizontal measurements.How do you avoid confusion? Make sure you know your manufacturer’s specifications and make sure you don’t lose track of your numbers while making a comparison.

Small display advantagesLaptops with small displays are frequently lighter and more compact. You can find models that still offer great resolution; small displays also generally consume less power compared to larger options.Mr. Ranjan selected laptop of compact size of 13 inches screen size which had 5 inches height and 1 inch thickness. He also ordered for a radiation shield for the screen and a fit well cover for his device. Both are to be charged at Rs.25 per square inch for the radiation shield and Rs.8 per square inch for the fit well cover.

6.1) How much will Mr. Ranjan pay for the screen shield?

6.2) What will be the cost of Fit well cover for his device?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea SPACE AND SHAPEContext Societal/ScientificItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 2


Description of Answer Key and Credits6.1) Full credit: 02

Cost of screen shield = Rs.1500Partial credit: 01To find the length = 12 inches, area 60 = sq.inches


6.2) Full credit: 02Cost of the cover is Rs.1232Partial credit: 01To find the TSA of cuboid as 154 sq.inches.

No Credit: 00


Domain: Mathematics literacy

Theme: Surface Area Class: IXExpected time: 10 Min.

Total credit: 02Description of Item

Text Image Table

GraphMap Poem

Learning outcome:(as per NCERT)

Find surface area of cylinder by using appropriate formulae.

13. ART FEST

It was decided to have an Art Festival involving different activities on the National Museum Day by museum authorities. In Hall-4 of the museum they arranged Paintings of that city artists. In Hall-3 of the museum they arranged stone and wooden sculptures of different city artists. In Hall-2 of the museum they arranged metal carvings of national artists. In Hall-1 of the museum they arranged jewellery Exhibition of international artists.

The dots in the table denote cylindrical pillars. The pillars of height 3.5 metre and diameter30 cm. The outer pillars of the halls are decorated with gold colour at the rate of Rs.20 /m 2while inner pillars of the hall are decorated with the silver colour at the rate of Rs.15 /m2.

13.1) What is the cost of painting in gold colour in the hall where city artists held their painting works?

FRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea SPACE AND SHAPEContext SocietalItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 2


Description of Answer Key and Creditsa) Rs.1188 Full credit: 2,

b) 59.4 sq.m Partial credit: 1

c) No credit: 0 For any other response

Name of the Teacher/Item Writer: K. GanesanDesignation: TGT (Maths)Email: [email protected] No: 9444666889Name of the Vidyalaya: AFS Avadi Chennai-55KVS Region: Chennai

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Text Image Table

GraphMap Poem



13. ART FEST

13.2) What is the cost of painting in silver colour in all the halls?




a) Rs.990 Full credit: 2 ,

b) 66sq.m Partial credit:1

c) No credit: 0 For any other response

Name of the Teacher/Item Writer:K.GanesanDesignation: TGT(Maths)Email:[email protected] No:9444666889

Name of the Vidyalaya: AFS Avadi Chennai-55KVS Region: Chennai

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Text Image Table

GraphMap Poem



13. ART FEST

13.3) What is the total number of pillars in the museum?



Description of Answer Key and Creditsa) 68 Full credit: 2,

b) No credit: 0 For any other response

Name of the Teacher/Item Writer: K. GanesanDesignation: TGT(Maths)Email: [email protected] No: 9444666889Name of the Vidyalaya: AFS Avadi Chennai-55KVS Region: Chennai




Text Image Table

GraphMap Poem


Finds surface area of cylinder by using appropriate formulae.

13. ART FEST

13.4) Observing the pattern, by taking ‘n’ as the hall number (n=1,2,3,4), what could be the formula you can arrive to find out the total pillars in each hall?



Description of Answer Key and Creditsa) (n+1)(n+2) Full credit: 2 ,

b) No credit: 0 For any other response

Name of the Teacher/Item Writer: K. GanesanDesignation: TGT(Maths)Email: [email protected] No: 9444666889Name of the Vidyalaya: AFS Avadi Chennai-55KVS Region: Chennai

Domain: Mathematics literacy Theme: Volume of cone, sphere and cylinder

Class: IXExpected time: 3 MIN.Total credit: 02

Description of Item Text Image

TableGraphMap Poem


The learner develops a relationship between Volume of cylinder, sphere and cone.

PRACTICE ITEM 1.1

SWEET ALCHEMY

The parlour offers flavours including Pabrai’s Nalen Gur Ice Cream, Kolkata meethapaan ice cream, rose petal ice cream, musk melon ice cream, tender coconut ice cream, Italian mascarpone cheese & candied fruit ice cream, freshly brewed south Indian coffee ice cream, chocolate ice cream in eight flavours using only naturally processed cocoa, six flavours of sugar-free ice creams with no added sugar and many more. The shop sells its products in 3 different shapes: a cylindrical bar, a spherical ball, and a cone. These 3 shapes are of the same height and radius, as shown in the picture.

Which of these choices would give you the most ice cream?(i) A full cylindrical bar or (II). A ball plus a cone(a) A cylindrical bar because it has more volume.(b) A ball plus a cone because the volume of the two is greater than just one.(c) Not enough information.(d) Doesn't matter. Both options have got the same amount

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster ConnectionsOverarching Idea OccupationalContext Relationships between volume of solidsItem Format MCQCognitive process InterpretingProficiency Level 2


Description of Answer Key and CreditsExplain expected answer and the respective credits.Both options have got the same amount 2π r3

F.C: 02P.C: [No partial credit]

Name of the Teacher/Item Writer: K. MAHADEVANDesignation: PGT(MATHS)Email: [email protected] No: 9445606533Name of the Vidyalaya: CLRI CHENNAIKVS Region: Chennai

Domain: Mathematics literacy Theme: Volume of combination of hemisphere and cylinder.



TableGraphMap Poem

Learning outcome:(as per NCERT).

The learners are able to identifyradius and heighy of a cyliner and hemisphere

Running is very taxing on your body. Whether you’re a sprinter or a long-distance runner, it’s important to understand that to perform at your peak potential, you need to supply your body with the proper nutrients.Sometimes, even with a great diet, the food we eat is not enough to provide the fuel we need. Supplements or vitamins for runners help to give that extra endurance boost, you need to maximize your performance and recover more rapidly.Hence Brinda went to a doctor and she prescribed some vitamin capsules.A capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. If the length of the entire capsule is 15 mm and the diameter of the capsule is 3 mm, how much medicine it can hold?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster ReflectionOverarching Idea SocietalContext Volume of combination of solidsItem Format Short response itemCognitive process Problem solving.Proficiency Level 3


Description of Answer Key and CreditsF.C: 99mm3.P.C: Proper substitution onlyN.C: Any other response

Name of the Teacher/Item Writer: K. MAHADEVAN, Designation: PGT(MATHS)Email: [email protected], Phone No: 9445606533Name of the Vidyalaya: CLRI CHENNAI, KVS Region: Chennai

Item 1.3 BEAUTIFUL SOUVENIR

Domain: Mathematics literacy Theme: Polynomials Class: IXExpected time: 10 Min.Total credit: 02


TableGraphMap Poem


The learners are able to identify the relationship between radius and edge of a cone and hemisphere respectively.

A souvenir is made by scooping out a hemispherical from one face of a cubical block (as shown in the Fig.) such that the diameter ‘a’ cm of the hemisphere is equal to side length of the cube. Find the surface area of the souvenir.

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea OccupationalContextItem Format Yes/no.Cognitive process InterpretingProficiency Level 3



F.C: 6a2+ π a2

4

P.C: 6a2+ π a2

2


1.4 TODDLERS PLAYING WITHBUILDING BLOCKS

Ramu and Somu are best friends and always play together. As a birth day gift,Ramu got building blocks from his friend. On Sunday while playing with cubes they made two cuboids in different sizes withequal 4 congruent cubes as shown in the given figure. 4 cubes are arranged to form cuboid A and cuboid B. Cuboid B's surface area is 288 larger than cuboid A's surface area. Find the volume of cuboid A.

Domain: Mathematics literacy Theme: Surface area and Volume of cube and cuboids



TableGraphMap Poem


The learners are able to identifydimesions of a cuboid A and cuboid B respectively

Mathematical Literacy

FRAMEWORK CHARACTERISTICSCompetency cluster ReproductionOveraching Idea Relationships between dimensions of cuboidContext Volume of Cuboid BItem Format Short response itemCognitive process Problem solving.Proficiency Level 3


Description of Answer Key and CreditsF.C: 6912 cm3

P.C: side length of the small cube=12 cm.


(1.5) BALLS IN TANKS

Three identical tanks are shown above. The spheres in a given tank are of the same size and packed wall-to-wall. If the tanks are filled to the top with water, then which tank would contain the most water?

A B C They'll all contain the same amount of water

Domain: Mathematics literacy Theme: Volume of cuboid and Sphere


Description of Item Text

ImageTableGraphMap Poem


The learners are able to anlyzeradius of spheres inserted in the tanks A, B and C respectively

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster ReflectionOveraching Idea Spatial.Context Reasoning.Item Format MCQCognitive process Interpreting.Proficiency Level 3


Description of Answer Key and Credits F.C: They'll all contain the same amount of water P.C: NO


Item (1.6): HEMI-SPHERICAL TANK

Water is essential for life and every citizen has a right to have safe and adequate drinking water. Drinking water is a public good. Therefore, everyone has the right to access potable drinking water. Water Tank/Reservoir are used to store treated water for supplying to users.A hemi-spherical tank of radius 105 cm is full of water. It is connected with a pipe which empties the tank at the rate of 4 litre per second. How much time will it take to empty the tank completely?

Domain: Mathematics literacy Theme: Class: IXExpected time: 05 Min.Total credit: 02


TableGraphMap Poem


To find the volume of a hemisphere and conversion of units.

Mathematical Literacy:FRAMEWORK CHARACTERISTICSCompetency cluster ConnectionsOverarching Idea SocietalContext Quantity.Item Format Short response itemCognitive process Problem solving.Proficiency Level 3


Description of Answer Key and CreditsF.C: 10 minutes (approx)P.C: Proper substitution:


Domain: Mathematical literacy

Theme: Volume of hemi-SphereCONTEXT : 1

Class: IXExpected time: 5 minutesTotal credit:02


TableGraphMap Poem

Learning outcome: (as per NCERT)

Students are expected to identify the formula and apply.

1. Rama got up early in the morning and asked for a cup of coffee to his mom. But his mom served the coffee in a hemispherical bowl of diameter 2cm. How much coffee Rama would have consumed?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea Changes and relationsContext SocietalItem Format Very Short Answer type Cognitive process InterpretingProficiency Level Level 1



Full credit: Formula- 23πr3 , Answer:2.09 cm3

Partial credit: Formula- 23πr3

Domain: Mathematics literacy Theme: Surface area of hemi-Sphere

CONTEXT : 1


Description of Item

Text Image

TableGraphMap Poem



2. Rama got up early in the morning and asked for a cup of coffee to his mom. But his mom served the coffee in a hemispherical bowl of diameter 2cm. By seeing the bowl, he wanted to apply the concept from previous day’s class, so he decided to find the surface area of the bowl. Could you help Rama in finding the surface area of the bowl in which coffee was served?



Description of Answer Key and CreditsFull credit: Formula- 2 πr2 Answer: 6.28 cm2

Partial credit: Formula- 2 πr2

No credit: For any other response

Domain: Mathematical literacy Theme: Surface area of Sphere Class: IX

CONTEXT : 2 Expected time: 10 minutesTotal credit:05

Description of Item

Text Image

TableGraphMap Poem



3. Priya is having a Mathematical project work in her school for which she requires 64 small metal balls, but she has only one big metal ball of radius 8cm. So she decides to melt the big ball and make it into 64 small metal balls of same size and arrange them for her project as shown in the figure. And also she decides to calculate the surface area of the each small ball. Calculate the surface area of each small spherical ball and help Priya?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea Changes and relationsContext SocietalItem Format Short Answer type Cognitive process InterpretingProficiency Level Level 2

Credit pattern :Full credit: 05Partial credit: 02No credit: 00

Description of Answer Key and CreditsFull credit Let the radius of small sphere be r cm∴ volume of 64 small spheres is equal to volume if 1 big sphere

64 x4πr3

=4π x 43

3 3⇒ 64r3 = 64⇒ r = 1Surface Area of small circle = 4 x π x 12 = 4π cm2 Partial credit: Finding r =1 No credit: For any other response

Domain: Mathematics literacy Theme: Volume of SphereCONTEXT : 2



TableGraphMap Poem



4. Priya is having a Mathematical project work in her school for which she requires 64 small metal balls, but she has only one big metal ball of radius 8cm. So she decides to melt the big ball and make it into 64 small metal balls of same size and arrange them for her project as shown in the figure. And also she decides to calculate the volume of the each small ball. Calculate the volume of each small spherical ball and help Priya?



Description of Answer Key and CreditsFull credit:

Volume of big Sphere= 4 π3 r3

= 4 π3 43

= 267.94 cm3

Volume of Small Sphere = 267.94/ 64 = 4.18 cm3

Partial credit: Finding Volume of big Sphere= 4 π3 r3

= 4 π3 43

= 267.94 cm3

Domain: Mathematics literacy Theme: Volume of SphereCONTEXT : 3



TableGraphMap Poem



5. Shyam was watching a group of students playing basketball in his school. He saw one student shooting the basketball into the basket correctly. On watching the ball go into the basket correctly Shyam got a thought that how much air the ball could hold if the ball had a diameter of 6cm. Help Shyam in finding the amount of air in the basketball.


Credit pattern :Full credit:02Partial credit:01No credit: 00


Full credit: Formula- 43 πr3 , Answer: 113.14 cm3

Partial credit: Formula- 43 πr3

No credit: For any other response

Name of the Teacher/Item Writer: K THANERAJ, Designation: PGT (Mathematics)Email:[email protected], Phone No: 8610859912Name of the Vidyalaya: KV Anna Nagar, KVS Region: Chennai

Domain: Mathematics literacy Theme: Surface Area Class: IXExpected time: 05minutesTotal credit: 02

Description of Item

Text Image

TableGraphMap Poem


Find the surface area of given sphere

GLOBE

1. In class 9th, Social science teacher was teaching the concept of ‘WORLD political’ with a Model globe. Children were comparing the areas of the continents. One boy told that if it is a plane figure, area can be found by using length and breadth. How to find the Curved surface area? Another boy told using the formula of Curved Surface Area of a Sphere. The Children measured the circumference at the middle of the Model globe using a thread as 66cm.What is the Total Surface area of the Model globe?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea Changes and relationsContext Societal Item Format Short answer typeCognitive process transformationProficiency Level Level 2


Full Credit: Total surface Area of the Model globe = 132cm2

Partial credit: To find the radius of the sphere =10.5cmNo credit: Any other response


Name of the teacher(s): M. Manivannan, Designation: TGT MathematicsEmail: [email protected], Phone no. : 9445368909Name of the Vidyalaya: KV Annanagar, KVS Region: Chennai

Domain: Mathematics literacy Theme: Surface Areas and Volumes

Class: IXExpected time: 05minutes


Text Image

TableGraphMap Poem


Find the surface area of given sphere

There was a painting competition conducted for the children of class 9 th during Art period. Speed, Accuracy and area of painting were the measures for the judgement. Two Children submitted at the same time with uniform performance. Each of them was given a coconut shell of same dimension. Both of them completed the task in half an hour at the rate of completion of painting 409.64cm 2 in an hour. If the outer width of each shell is 8.4cm, find the inner radius of each shell?

Mathematical Literacy FRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea Changes and relationsContext Societal Item Format Short answer typeCognitive process transformationProficiency Level Level 2

Full Credit: Inner radius of the shell = 3.5cm Partial credit: As deservedNo credit: Any other response

Credit pattern:Full credit: 03Partial credit: 02 or 01 as deservedNo credit: 00

Name of the teacher(s):.M.ManivannanDesignation:TGTMathematicsEmail: [email protected] no. :9445368909Name of the vidyalaya: KV AnnanagarKVS Region: Chennai


Class: IXExpected time: 05minutesTotal credit: 02

Description of Item

Text Image

TableGraphMap Poem


Find the inner surface area of the basket.

Kiruba was maintaining a small animal farm in which some chickens were there. She made 2 baskets of hemispherical shape with the total volume of 4.851m3.Find the inner surface area of one basket?

Full Credit: Inner surface area of the basket=6.93m2

Partial credit: To find the radius as 1.05mNo credit: Any other response

Credit pattern :Full credit:02Partial credit: 01 as deservedNo credit:0

Name of the teacher(s):.M. ManivannanDesignation: TGT MathematicsEmail: [email protected] no. : 9445368909Name of the Vidyalaya: KV AnnanagarKVS Region: Chennai

Domain: Mathematics literacy Theme: Surface Areas and Class:IX

Volumes Expected time: 05minutesTotal credit: 02

Description of Item

Text Image

TableGraphMap Poem


Find the inner surface area of the globe

In an all faith prayer centre a globe was made with the volume of 38.808m 3. Find the inner surface area of the globe.

Full Credit: Inner surface area of the globe=55.44m2

Partial credit: to find the inner radius as 2.1mNo credit: Any other response

Credit pattern:Full credit: 02Partial credit: 01 as deservedNo credit: 00

Name of the teacher(s):M. ManivannanDesignation: TGT MathematicsEmail: [email protected] no. : 9445368909Name of the Vidyalaya: KV AnnanagarKVS Region: Chennai

Domain: Mathematics literacy Theme: Surface Areas and Class: IX


Description of Item

Text Image

TableGraphMap Poem


Find the volume of each colour of clay required to make the following model of hemisphere.

A toy maker was making the models of fruits and selling. One among the models was as above. He made the above model with the clay of Red, White and Green colours and volumes in the proportion 7:5:3 respectively. The surface area of the toy was found to be 1039.5cm2.Find the volume of each colour of clay used to make 100 such models.

FRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea Changes and relationsContext Societal Item Format Short answer typeCognitive process transformationProficiency Level Level 1

Full Credit: Volume of Red clay: 169785cm3

Volume of Green clay: 121275cm3

Volume of Green clay: 72765cm3

Partial credit: As deserved No credit: Any other response

Credit pattern :Full credit:03Partial credit: 02 or 01 as deserved No credit:0

Name of the teacher(s): M. PunithamaniDesignation: TGT MathematicsEmail: [email protected] no.: 7418237857Name of the Vidyalaya: KV OCF AvadiKVS Region: Chennai


Class: IXExpected time: 05minutes


Text Image

TableGraphMap Poem


Find the diameter of each orange fruit.

In a hospital a group of patients have to be given orange juice daily.200 oranges of uniform volume are used daily to get juice. Theyield of juice is 50% of the total volume of the fruits and the volume of juice obtained is 11304cm3. Find the diameter of each orange fruit.


Full Credit: Diameter of each orange fruit: 3cmPartial credit: 02 or 01 as deservedNo credit: Any other response

Credit pattern:Full credit: 03Partial credit: 02 or 01 as deservedNo credit: 0

Name of the teacher(s): M.PunithamaniDesignation:TGT MathematicsEmail: [email protected] no.: 7418237857Name of the vidyalaya: KV OCF AvadiKVS Region: Chennai



Description of Item

Text Image

TableGraphMap Poem


Find the volume of the model sphere.

A group of children in 9th std made a model of sphere with the surface area of a sphere 12474cm2as project work. Calculate its volume.


Full Credit: Volume of the sphere: 14553cm3

Partial credit: 01 to find radius as 31.5cmNo credit: Any other response


Name of the teacher(s): M. PunithamaniDesignation: TGT MathematicsEmail: [email protected] no.: 7418237857Name of the Vidyalaya: KV OCF AvadiKVS Region: Chennai



Description of Item

Text Image

TableGraphMap Poem


Find the number of guests who can be served gheer.

In a birthday party guest were served gheer. A hemispherical bowl of internal diameter 30cm contains gheer full is to be filled in a hemispherical cup of radius 4.5cm.For how many guests the gheer could be shared with.


Full Credit: No of guests can be provided with gheer: 296Partial credit: 01No credit: Any other response


Name of the teacher(s): M.PunithamaniDesignation: TGT MathematicsEmail: [email protected] no.: 7418237857Name of the vidyalaya: KV OCF AvadiKVS Region: Chennai

Domain: Mathematical Literacy Theme: Volume of Cone Class: IX

Expected Time: 07 minTotal Credit:02

Description of item. Text Image

TableGraphMapPoem

Learning Outcome:(As per NCERT)Calculating volume of a cone.

1.1. HAVE A NICE COFFEE.

Mr. Gopal has a super –jumbo-sized drip coffee maker. The beverage is produced as a hot water filters through a cone-shaped vessel containing coffee grounds. The cone has a height of 3 inches and diameter of one foot. Assuming that the cone is filled with water, and the water is dripping out at a rate of 10 cu. inch per minute, how long will it take for all of the water to pass through?

Mathematical LiteracyFRAME WORK CHARACTERISTICSCompetency Cluster Procedural fluencyOverarching Idea Space and ShapeContext VolumeItem Format Short ResponseCognitive Process Problem SolvingProficiency Level 5

Credit Pattern:Full Credit: 02.Partial Credit: 01.No Credit: 0

Description of Answer Key and Credits:Explain expected answer and the respective credits:Finding correct Volume as 113.14 cu. Inch Partial credit – 01Finding the total time taken to drip out 11.31 min – Full credit – 02

Name of the Teacher: N. S. Subramanian., Designation: PGT (Math)Email: [email protected]., Phone Number: 8146157391.Name of the Vidyalaya: KV CLRI., KVS Region: Chennai.

Domain: Mathematical Literacy Theme: Volume of Cone Class: IXExpected Time:07 minTotal Credit:02


TableGraphMapPoem


1.2 HURRYUP YOURTIME IS OUT

You must answer a trivia question before the sand in the timer falls to the bottom. The sand falls at a rate of 50 cubic millimetres per second. How much time do you have to answer the questions?



Description of Answer Key and Credits:Explain expected answer and the respective credits:Finding correct Volume as 2514.8 cu.mm Partial credit – 01Finding the time taken to answer the question 50.3 sec – Full credit – 02

Name of the Teacher: N. S. Subramanian., Designation: PGT (Math)Email: [email protected]., Phone Number: 8146157391.Name of the Vidyalaya: KV CLRI., KVS Region: Chennai.

Domain: Mathematical Literacy Theme: Volume of Cone Class: IXExpected Time:10minTotal Credit:02


TableGraphMapPoem

Learning Outcome:(As per NCERT)Connecting volume of a cone to find the variables.

1.3 HAVE AN AWESOME LEMONADE

LEMONADE STAND: You have 10 gallons of lemonade to sell. (1 gal = 3785 cm3)If each customer uses one paper cup. How many paper cups will you need?



Description of Answer Key and Credits:Explain expected answer and the respective credits:Finding Volume correct 184.38 cm3 Partial credit -01Finding the total number of cups 205 cups – Full credit-02

Name of the Teacher: N.S.Subramanian.Designation: PGT (Math)Email: [email protected] Number: 8146157391.Name of the Vidyalaya: KV CLRI.KVS Region: Chennai.

mailto:[email protected]

Domain: Mathematical Literacy Theme: Volume of Cone Class: IXExpected Time:04 minTotal Credit:02


TableGraphMapPoem

Learning Outcome:(As per NCERT)Connecting volume of a cone to find the variables


The cups are sold in packages of 50. How many packages should you buy?



Description of Answer Key and Credits:Explain expected answer and the respective credits:Finding the answer as 5 – Full credit – 02 For all other answers no credit.

Name of the Teacher: N. S. Subramanian.Designation: PGT (Math)Email: [email protected] Number: 8146157391.Name of the Vidyalaya: KV CLRI.KVS Region: Chennai.

Domain: Mathematical Literacy Theme: Volume of Cone Class: IXExpected Time:06minTotal Credit:02


TableGraphMapPoem



How many cups will be left over if you sell 80% of the lemonade?



Description of Answer Key and Credits:Explain expected answer and the respective credits:Finding 20% of left over lemonade as 7570cm3- partial credit-01Finding the number of cups left as 41 – Full credit-02

Name of the Teacher: N. S. Subramanian.Designation: PGT (Math)Email: [email protected] Number: 8146157391.Name of the Vidyalaya: KV CLRI.

Domain – Mathematical Literacy Theme – Volume of Cubes and cuboid

Class – IXExpected Time – 10 minTotal Credit-02

Description of Items Text Image

Table Graph

MapPoem

Learning Outcomes – As per NCERT Syllabus Relate combined length of fishes with the capacity of

aquarium Convert gallons to litres.

AQUARIUM1.1

Avinash is a student of 8 th standard. Every year in the month of August, the school arrange Study Tour. But, this year due to COVID-19, the schools are closed and classes are all online. One day during the Online class, Avinash’s class teacher announces about the Virtual Tour to an Aquarium. He was very enthusiastic about the virtual tour. On the day of prsentation his class teacher takes them to “Virtual Tour of Dubai Aquarium”.

After the tour he decided to buy an aquarium. The graph shows tank sizes using a rule that relates the capacity of the tank (in gallons) to the combined lengths of the fish (in inches) it can hold.

2 4 6 8 10 120

2

4

6

8

10

12

14

Length (in inches)

Capa

city

( in

Gallo

ns)

1. He decided to buy three Cory Cat fish, each of length 1 inch, two Neon tetras, each of length 1.5 inches and two Zebra Danies, each of 2 inches. What is the smallest capacity tank he can buy? (In Gallons).............................................................................................................................……………………………………………………………………………………………

2. He buys an aquarium of the capacity 46.5 litres. (1 gallon = 4.5 litres)True / False.

Mathematical LiteracyFramework CharacteristicsCompetency Cluster Performing specific calculationsOverarching Idea QuantityContext PersonalItem Format Short response , T/FCognitive Process Interpret Proficiency Level 2

Credit Pattern: Full Credit: 02Partial Credit: 01No Credit: 00

Description of answer key and credits.1. 11 gallons2. False

FC- both correct answerPC- any one answer is correct

Name of the teacher: PrajishaDesignation: TGT MathsEmail: [email protected] No: 9495916371Name of the Vidyalaya: KV AFS SULURKVS region: CHENNAI

1.2

Domain – Mathematical Literacy Theme – Volume of Cubes and cuboid


Description of Items Text

Image Table

GraphMapPoem

Learning Outcomes – As per NCERT Syllabus Volume of Cuboid

Help Avinash to complete the tables of details of Aquarium

Length (cm) Breadth (cm) Height (cm) Capacity (litres)50 40 30 a45 b 40 5455 35 c 77

Mathematical Literacy

Framework CharacteristicsCompetency Cluster Solving VolumesOverarching Idea QuantityContext Volume of cuboidItem Format Short response Cognitive Process FormulateProficiency Level 3


Description of answer key and credits.

a. 60b. 30c. 40

FC- All 3 are correctPC- any one answer is correct

Name of the teacher: PrajishaDesignation: TGT MathsEmail: [email protected] No: 9495916371Name of the Vidyalaya: KV AFS SULURKVS region : CHENNAI

1.3

Domain – Mathematical Literacy

Theme – Volume of Cubes and cuboid


Description of Items Text Image

TableGraphMapPoem


1. Avinash selected an aquarium, whose two-fifth is filled with water. After taking it home, he added 16 litres of water. Now it is two-third filled with water. Find the height of aquarium if its length and width are 50 cm and 40 cm respectively.………………………………………………………………………………………………………………………………………………………………………………………….…………………………………………………………………………………………….…………………………………………………………………………………………….

2. After few days he dropped 500 pebbles each of volume 5 cubic cm, a solid toy treasure chest shaped like a rectangular prism measuring 14 cm x 10 cm x 8 cm and a plant of volume 380 cubic cm. The level of water raise is a. 4cmb. 2cmc. 6cmd. 8cm

Mathematical LiteracyFramework CharacteristicsCompetency Cluster Using mathematics to solve problemOverarching Idea QuantityContext Volume of cuboidItem Format Short response, Complex MCQCognitive Process Employ and InterpretProficiency Level 3


Description of answer key and credits.

1. 30 2. B (2 cm)

FC- Both are correctPC- any one answer is correct


1.4

Domain – Mathematical Literacy

Theme – Volume of Cubes and cuboid


Description of Items Text

ImageTableGraphMapPoem


Avinash bought a jar of fish-food flakes, rectangular in shape of dimensions 6cm x 3cm x 4cm, and the food will last for approximately 110 days. He wanted to empty the food into small cubical jars of dimension 2 cm.

1. The number of cubical jars required is a. 10b. 8c. 9d. 12

2. The food in one cubical jar can be approximately used fora. 12b. 9c. 8d. 10.

Mathematical LiteracyFramework CharacteristicsCompetency Cluster Performing specific calculationsOverarching Idea QuantityContext Volume of cubes and cuboidsItem Format Simple MCQCognitive Process InterpretProficiency Level 4


Description of answer key and credits.1. c 2. a

FC- Both are correctPC- any one answer is correct


IT’S SARAH’S BIRTHDAY PARTY

Birthday Wishes by Jake:Another birthday, another year,May you have your problems that disappearMay you have healthAnd a bit of wealthMay you shareWith those who careMay the coming yearBe one of good cheer!!!

Hey Sarah…looking for your giftSolve this riddle Behold. You will cherish it for life

Iam part of a dessert, Kids love me,Hey.here comes Joker Uncle,Do you wear me?The traffic Police takes my helpHe says…O dear…What would I do without you…

Iam a part every Birthday partyKids sport it on their crown,Without it they frown,They love clicking selfies with me…Mm..my shape is hidden in these linesCan you find me out.?

Q1.What’s the shape of the gift that Jake is speaking about in his birthday wishes to Sarah?

Mathematical Literacy:

FRAMEWORK CHARACTERISTICSCompetency Cluster Conceptual UnderstandingOverarching Idea SPACE AND SHAPEContext SOCIETALItem Format Short Answer TypeCognitive Process InterpretingProficiency Level Level 1

Credit pattern:Full Credit:02Partial Credit: 00No Credit: 00

Description of Answer Key and creditsFULL CREDIT:02, THE GIFT IS CONE SHAPED CAPSNO CREDIT: For any other response

Name of Teacher M. A. Rasheetha BegumDesignation: TGT MATHSEmail: [email protected] no: 8668180879Name of Vidyalaya: Kendriya Vidyalaya Gill NagarKVS REGION: CHENNAI

Domain: Mathematics literacy Theme: VOLUME OF A Class: IX

CYLINDER Expected time: 05 MIN.Total credit: 02

Description of Item√ Text


Learning outcome: To find the volume of cylinder.(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Procedural fluencyoverarching Idea Mathematical understandingContext Volume of cylinderItem Format Short response itemCognitive process Problem solvingProficiency Level 1

Thirumalai Nayakar palace is the 17th century palace, erected in 1636 by King Thirumalai Nayakar, a king of Madurai and Nayakar dynasty in the city of Madurai, Tamilnadu, India. This palace is a classic fusion of Dravidian and Rajput styles. This palace has many pillars which are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10m, how many concrete mixtures would be used to build 14 such pillars.


Description of Answer Key and Credits14 pillars would need 17.6 m3 of concrete mixture. (Full credit)Volume of a cylinder = π r2h (Partial credit)Any other response (No credit)

Name of the Teacher/Item Writer: S.JAYARAMAN, Designation: PGT(MATHS)Email: [email protected], Phone No: 9427523022Name of the Vidyalaya: no1, OE, Trichy, KVS Region: Chennai

Domain: Mathematics literacy Theme: Comparing volume. Class: IXExpected time: I5 MIN.Total credit: 02

Description of Item√ Text√ Image

TableGraphMap Poem

Learning outcome: To compare the volume of different figures.(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Adaptive reasoningOverarching idea Mathematical RelationshipContext VolumeItem Format Short response item.Cognitive process Decision makingProficiency Level 3

Two milkmen are using different types of mug to serve milk to the customers. The first milkman uses mug A and the second one uses mug B to serve the milk. The inner diameter and the height of the mugs are 5 cm and 10 cm respectively. Some customers prefer to buy milk from first and some from second. In mug B, the height of the conical region is 1.5 cm.

1) If you are one of the customers which milk man will you prefer to buy the milk from? Why.

2) Which mathematical concept is used in this?

Mug A Mug B


Description of Answer Key and Credits(1) Second. Because capacity of mug A is 163.54 cm3 and mug B is 186.43 cm3.(2) Volume. (full credit)Find the volume of cylinder (Partial credit)

Name of the Teacher/Item Writer: S.JAYARAMANDesignation: PGT(MATHS)Email: [email protected] No: 9427523022Name of the vidyalaya: no1, OE, TrichyKVS Region: Chennai.

Domain: Mathematics literacy Theme: Volume of cylinder Class: IXExpected time: 05 MIN.Total credit: 02



Learning outcome: To find the volume of a cylinder(as per NCERT) .

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Procedural fluencyOverarching Idea Mathematical understandingContext Volume of a cylinderItem Format Short response itemCognitive process MemoryProficiency Level 1

Thomas loves tomatoes. He plans to fill a cylindrical container with soil to grow his own tomato plants. The base diameter and height of the container is 20cm each. How much soil will the container hold? If he plans to use a conical container, how much soil will this container hold?


Description of Answer Key and Credits2000π cm3, 666.66π cm3 (Full credit)V = π X 10 X 10 X 20 (Partial credit)

Name of the Teacher/Item Writer: S.JAYARAMANDesignation: PGT(MATHS)Email: [email protected] No: 9427523022Name of the Vidyalaya: no1, OE, TrichyKVS Region: Chennai

Domain: Mathematics literacy Theme: Volume of cone Class: IX

Expected time: I0 MIN.Total credit: 02



Learning outcome: To find the volume of a cone.(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea Mathematical understandingContext Volume of a coneItem Format Short response itemCognitive process InterpretingProficiency Level 3

Ravi has a super- jumbo-sized drip coffee maker. The beverage is produced as hot water filters thorough a cone- shaped vessel containing coffee grounds. The cone has a height of 3 inches and diameter of 1 foot. Assuming that the cone is filled with water and the water is dripping out at a rate of 10 cu. in. per minute, how long will it take for all the water to pass through?



Time = 1/3 X3.14 X15 X 15 X 7.5

10 X 2.5 X 2.5X2.5 = 11.31 minutes (Full credit)

Find the Volume of the cone (Partial credit)


Domain: Mathematics literacy Theme: Volume of cylinder Class: IXExpected time: I0 MIN.Total credit: 02



Learning outcome: To find the volume of a cylinder(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Procedural competencyOverarching Idea Mathematical relationshipContext Volume of cylinderItem Format Short response itemCognitive process Sequential processing Proficiency Level 3

People living in Rajasthan sometimes find that the water in their swimming pools become uncomfortably warm during the summer months. This situation can be rectified by adding ice cubes to the pool. The following authentic formula can be used to determine the approximate number (N) of five pound bags of ice required to reduce the temperature of a pool by D degrees Fahrenheit if the volume of the pool is V cubic feet. N = 0.06125DV. Meena’s pool is circular bottom with a diameter of 24 feet and height of 4 feet. Using the formula, how many bags of ice are required to reduce the temperature from 850 to 700. (Use π = 3.14)


Description of Answer Key and CreditsN = 0.06125 X 15 X 3.14 X 12 X 12 X 4 = 1661.68So 1662 bags are required (Full credit)To find volume of the cylinder (partial credit)


Domain: Mathematics literacy Theme: Volume of cylinder Class: IX

Expected time: I0 MIN.Total credit: 02



Learning outcome: To find the volume of cylinder(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Adaptive reasoningOverarching Idea Mathematical understandingContext Volume of the cylinderItem Format Short response itemCognitive process VisualizationProficiency Level 4

Johnson has noticed that when a garden hose is left exposed to the summer sunshine, the water resting within the hose becomes heated. This inspires Johnson to construct a low tech solar water heater. He reasons that if he connects a sufficient length of hose and leaves it in a sunny spot, this will provide an ample supply of hot water.

He estimates that the drum of his washing machine is a cylinder whose diameter is 17 inches and height is 10 inches. Based on that assumption, how many linear feet of half- inch diameter water hose would be required in order to hold enough water to fill the drum of the washing machine?


Number of water hose required = 22/7 X17 /2 X17 /2X 1022/7 X 1/4 X1 /4 X 12 = 963.33

= 964 Water hose required (Full credit) (02)Volume of drum of the washing machine = 22/7 X 17/2 X 17/2 X10(Partial credit)(01)

Name of the Teacher/Item Writer: S.JAYARAMANDesignation: PGT (MATHS)Email: [email protected] No: 9427523022Name of the Vidyalaya: No. 1, OF, TrichyKVS Region: Chennai.




Learning outcome: To find the volume of cylinder(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Adaptive reasoning.Overarching Idea Mathematical understandingContext Volume of the cylinderItem Format Short response item.Cognitive process Visualization.Proficiency Level 3

Bharath petroleum decided to create one mile of pipeline to transport crude oil. In the general body meeting, Bharath petroleum comes to the conclusion that it will order crude oil from ONGC who provide crude oil in barrels.

Each barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in one mile of a pipeline that has an inside diameter of 6 inches and is completely filled with oil?

How much is one mile of oil in this pipeline worth at a price of Rs.65000 per barrel?

Description of Answer Key and CreditsI feet = 12 inch1 mile = 5280 feet

No of barrels required = 3.14 X 1/4 X1/ 4 X 5280

5.61 = 184.7

So number of barrels required = 185 (Partial credit) (01)Cost = 185 X 65000 = Rs. 1,20,25,000 (Full credit) (02)(or)Volume of pipeline (Partial credit)


Domain: Mathematics literacy Theme: Volume of the cone. Class: IXExpected time: I5 MIN.


√ TextImageTableGraphMap Poem

Learning outcome: To find the volume of cone(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Conceptual understandingOverarching Idea Change and relationship Context Volume of coneItem Format Short response itemCognitive process InterpretingProficiency Level 3

In a building construction site, the sand is filled in jute bags. One of the jute bags had a cut through which the floor on which the bag was kept, auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the amount of sand and therefore measure the circumference of the base and the length of both sides of the cone (over the top).

What is the volume of the sand cone, if the circumference of the base is 6m and the length oftwo sides together are 6m?

Description of Answer Key and CreditsVolume = 2.7 m3 (Full credit) (02)r = 6/2π = 0.95m (Partial credit) (01)(or)

h2 =364 – r2 ( Partial credit)


Domain: Mathematics literacy Theme: Volume of cone Class: IXExpected time: I5 MIN.Total credit: 02



Learning outcome: To find the volume of cone(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Procedural fluencyOverarching Idea Mathematical understanding Context Volume of coneItem Format Short response itemCognitive process Sequential ProcessingProficiency Level 2

A silo is shaped like a cone and contains wheat. The radius is 10 feet and the height is 15 feet.If the silo can release wheat from its bottom at the rate of 25 cubic feet per minute, how longwould it take for the silo to empty fully? Round your answer to the nearest minute, use theapproximate value of π, that is 3.14.


Description of Answer Key and CreditsTime take = 1570/25 = 63 minutes (Full credit)Volume of silo (Partial credit)





Learning outcome: To find the volume of cylinder.(as per NCERT)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Procedural fluencyOverarching Idea Mathematical understandingContext Volume of cylinderItem Format Short response itemCognitive process Problem solving.Proficiency Level 2

You are entering a pancake eating contest. Each plate has stack of pancakes 9 cm high. Each pancake has a diameter of 5 cm. If your stomach can hold about 1 litre, about how many plates of pancakes can your stomach hold?



Number of plates = 1000

3.14 X 2.5 X 2.5X 9 = 6(approx) (Full credit)

Volume of each stack of pancakes (Partial credit)

Name of the Teacher/Item Writer: S.JAYARAMANDesignation: PGT (MATHS)Email: [email protected] No: 9427523022Name of the Vidyalaya: no1, OE, TrichyKVS Region: Chennai.

Domain: Mathematics literacy Theme: SURFACE AREA AND VOLUMES

Class: IXExpected time: I0 MIN.

Total credit: 02

Description of Item› Text› Image› Table

GraphMappoem

Learning outcome:(as per NCERT)Finding the volume of cylinder

UNIT 1: MAKING OF BATTERYThere are three main components of a battery: two terminals made of different chemicals; the anode and the cathode; and the electrolyte which separates these terminals.On an average, 25% of the battery is made up of steel (casing). 60% of the battery is made up of a combination of materials like zinc (anode), manganese (cathode) and potassium. The remaining 15% by weight is made up of paper and plastic (label and protective cover).

1.1 Approximately how much steel is required to make 100 AAA batteries?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext ScientificItem Format Short answerCognitive process InterpretingProficiency Level 3

Credit pattern: Full credit: 02 Partial credits: 01 No credit: 00

Description of Answer Key and Credit

FC: VOL of 1 battery = 227 ×

10.52

10.52×44.5 =3854.81mm3

Vol of steel = 25

100 ×3854.81 × 100 = 96.37cm3

PC: vol of battery 3854 mm3



Total credit: 02 Description of Item

› Text› Image

TableGraphMappoem


UNIT 2: BIG PIPESA pipe manufacturer has 690cubic feet of iron to make into pipe that has an inside radius of 2 feet. The volume of iron in a pipe is the length of the pipe multiplied by the cross sectional area.

2.1 If the manufacturer needs to cast 2 inch thick pipes, what is the length of the pipe can be produced?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext OccupationalItem Format Short answerCognitive process Problem posing and solvingProficiency Level 3

Credit pattern:Full credit: 02Partial credit: 01No credit: 00


FC: vol of iron = 690=227 [(2.5)2 – 22] h =97.6ft

PC: 227 [(2.5)2 – 22] h = 690



Total credit: 02

Description of Item› Text› Image

TableGraphMappoem

Learning outcome:(as per NCERT)Finding the volume of cylinder and hemisphere

UNIT 3: TRASH CAN

3 Trash can manufacturer is designing a new trash can in the shape of a cylinder with a hemispherical top. The can must be 4feet tall and 2ft wide.3.1 How much trash it can hold?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext OccupationalItem Format Short answerCognitive process InterpretingProficiency Level 3



FC: vol of can=vol of cyl +vol of hs =πr2h+23πr3 =

227 ×1×1×4 +

23 ×

227 ×1×1×1 =

227 (4+

23 )=11.5 ft3

PC= vol of cyl +vol of hs =πr2h+23πr3

NC: Any other response


Class: IXExpected time: 05 MIN.


› Text› Image

TableGraphMappoem

Learning outcome:(as per NCERT)Finding the volume of cylinder and hemisphere

UNIT 4: GRAIN SILO DESIGN

A farmer constructs a grain silo in the shape of a cylinder with a hemispherical top. The silo must be 50ft tall and have a diameter of 20ft.Recall that the volume of cylinder with radius r and height his πr 2h and the

volume of sphere with radius r is 43 πr3.

4.1 How much money he gets if he sells grains for Rs.21 per cubic feet?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext OccupationalItem Format Short answerCognitive process Problem solvingProficiency Level 3



FC: vol of cyl +vol of hs =πr2h+23πr3 =

227 ×10×10×50 +

23× 22

7 ×10×10×10= 374000

21

Amt he gets=374000

21 × 21=Rs.374000

PC: Vol=374000

21 ft3

Domain: Mathematics literacy Theme: SURFACE AREA AND Class: IX

VOLUMES Expected time: I0 MIN.Total credit: 02

Description of Item› Text› Image

TableGraphMappoem


UNIT 5: CLASS CANDLES

Suresh is planning to make and sell 3 different sizes of cylindrical candles. He buys one cubic metre of candle wax for Rs.20 to make 5 candles of each size.5.2 He wants to make a profit of Rs.100. Which of the following prices of candles will be appropriate?

a) Rs.10, Rs.8, Rs.6 b) Rs.10, Rs.8, Rs.5 c) Rs.10, Rs.9, Rs.6 d) Rs.12, Rs.8, Rs.6

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext OccupationalItem Format MCQCognitive process InterpretingProficiency Level 3


Description of Answer Key and CreditsFC: Selling price=Rs.120 No. of sets=5Each set should be sold for 120/5=RS.24.. Option a)NC: Any other response


Class: IXExpected time:5 MIN.


› Text› Image

TableGraphMapPoem

Learning outcome:(as per NCERT)Finding the volume of cylinder and cuboids

UNIT 6: HAY BALES

A traditional “square” bale of hay is actually in the shape of a rectangular prism. Its dimensions are 2 feet by 2 feet by 4 feet. Approximately how many “square” bales contain the same amount of hay as one large “round” bale?




FC: No. of square hay =volofcyl

volofcuboid

=227×2×2×5

2×2×4=

5514 =3.9=4(approx)

PC: No. of square hay =volofcyl

volofcuboidNC: Any other response




› Text› Image

TableGraphMappoem

Learning outcome:(as per NCERT)Finding the volume of cylinder and sphere

UNIT 7: THIRSTY CROW

A thirsty crow wants to raise the level of water in a cylindrical container so that it can reach the water with its beak. The container has diameter of 2inches and a height of 9 inches. The water level is currently at 6 inches. The crow can reach the water if it is 1inch from the top of the container. In order to raise the water

level, the crow puts spherical pebbles in the container. If the pebbles are approximately 12 inch in diameter,

what is the fewest number of pebbles the crow needs to drop into the container in order to reach the water?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext socialItem Format Short answerCognitive process Problem solvingProficiency Level 5



FC: No. of pebbles= volofwatertoraisevolof 1 pebble

=

227×1×1×2

43× 22

7× 1

4× 1

4× 1

4

= 96

PC: : No. of pebbles= volofwatertoraisevolof 1 pebble





› Text› Image

TableGraphMappoem


UNIT 8: THIRSTY COW

A farmer has a water tank for cows in the shape of a cylinder with radius of 7 ft and a height of 3 ft. The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity. What is the volume of the tank when the sensor turns on?



Description of Answer Key and CreditsFC: vol of water= 20%of vol of tank

= 20100×

227 ×7×7×3 =

22×7×35 =92.4ft3

PC: vol of water= 20%of vol of tank = 20

100πr2h



Class: IXExpected time: 5 MIN.


› Text› Image

TableGraphMappoem


UNIT 9: WAFFY CHOCO ROLLS

Janani buys her favourite waffychoco rolls. It contains cylindrical shaped choco rolls packed in cylindrical box. She has 2 other siblings. Radius of choco rolls is 0.5 cm and length is 15cm. The radius and height of the cylindrical box is 3cm and 15cm.9.1 How many choco rolls will each child get?

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext socialItem Format Short answerCognitive process Interpreting

Proficiency Level 3



FC: no. of choco rolls=

227×3×3×15

227×0.5×0.5×15

=36

Each will get 12.

PC: no. of choco rolls=

227×3×3×15

227×0.5×0.5×15



Class: IXExpected time:5 MIN.


› Text› Image

TableGraphMappoem


UNIT 10: PROTEIN POWDER FOR HEALTH

Ankit plans to be in diet, so he consults his friend. He asks him to try protein powder which he had. The box is exactly half full. The radius and height of the box is 3.5cm and10cm.His friend directs him to add milk three times the quantity of powder.10.1 How much litres of milk should Ankit buy? (1 cm3 = 0.001 litre)

Mathematical LiteracyFRAMEWORK CHARACTERISTICSCompetency cluster Strategic competenceOverarching Idea QuantityContext personalItem Format Short answerCognitive process InterpretingProficiency Level 3



FC: vol of powder = 12×

227 ×3.5×3.5×10 = 192.5

Quantity of milk = 3×192.5×0.001=0.578litres

PC: vol of powder = 12×

227 ×3.5×3.5×10

Name of the Teacher/Item Writer : S.VALANTINA PRIYADHARSHINIDesignation : TGT (MATHS)Email : [email protected] No : 9841930432Name of the Vidyalaya : Kendriya Vidyalaya No1, OE, TrichyKVS Region

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