math coaching1 2ndbooklet(final)

7/30/2019 Math Coaching1 2ndbooklet(FINAL)

1/13

PROBLEM

A Polar Equation sinar represents a CIRCLE TANGENT FROM XAXIS

PROBLEM

A cube with vertex at the midpoint of the upper edge creates a pyramid inside the cube. What is the

total surface area?

Slant height h1: Slant height h2:

3137.118888

22

1

222

1

hh

9443.84848

22

2

222

2

hh

A1=AVCD A2=AVBC=AVAD

2548.453137.1182

11 A 7772.359443.88

2

12 A

A3=AVAB A4=AABCD=ABASE

32882

13 A 648

2

4 A

212.8092

AA2AAAreaSurfaceTotal 4321

PROBLEM

A roof of a galvanized aluminium rest house. Sides are 12m with a height of 6m. (a) Find the volume of

the galvanized aluminium roof. (b) Find the lateral area with a slant height of 10m.

(a)

3

2

288

6123

1

3

1

m

bhV

(b)

2240

101242

1

2

1

m

x

hPA SBL

PROBLEMA spherical ball with a radius of 14cm was drop on a cone with a depth of 20cm. Find the height from

the base of the cone to the point of tangency of the ball and the cone.

4 V 4

D 8 C

h1h2

A B


2/13

h=?

4131.24

1420

8

222

AB

AB

ODh

5539.6

4131.24

208

20

8

OD

AB

OD

cmh

h

ODh

5539.14

85539.6

8

PROBLEM

A trough which is triangular ends lie in parallel rectangle which is 50cm by 150cm. If the altitude is

40cm. What is the depth of the water if the volume is 12 liters?

hx

h

x

4

5

40

50

3137.11

1504

5

2

112000

)150(2

1

h

hh

xhV

PROBLEM

A rectangular parallelepiped whose length is 4m and 5m and the altitude is 6m. What is the area of the

cross section of the opposite edges of the parallelepiped?

O 8

D

8

14cm 14cm

C A

h

20cm

B

150 40

50

X

h

4 6

x

5


3/13

41

5422

x

x

242.38

641

mA

A

xhA

PROBLEM

A rectangular parallelepiped whose dimension is in the ratio 1:3:4. If the volume is 9000cu.m. What isthe longest dimension?

09.9

129000

43..9000

3

x

x

xxxmcu

LWHV

m

x

34.36

09.944

PROBLEM

A trapezoidal figure has an altitude of 40cm and a length of 72cm. The upper base is 25cm. and thelower base is 37cm. What is the volume of the figure?

389280

724037252

1

cmV

V

PROBLEM

When it rains 10cm. water fell. Determine the volume of the water fell on a level 10 hectare golf

course.

2

2

1000000000

1

100.100000

1

.1000010

cmA

m

cmmsqA

hectare

msqhectareA

3

3

10000000

10001101000000000

mmV

cmV

PROBLEM

A crown hat has a base of 90cm2

and depth of 10cm. If the head covers 2/3, find the area for

ventilation.

72

25

40

37


4/13

3

3

3

2

300nVentilatioofArea

9003

1nVentilatioofArea

900

1090

cm

cm

cmV

cmcmV

BhV

PROBLEM

If a smoke stick of a boat is 5m in height and it was sometime filled with 20cm3

of smoke, find the

lateral area ignoring the thickness.

2437.35

5128.12

2

mL

L

rhL

PROBLEM

How much material should be used in making 2500 dice with edge of 3cm.

67500

250027cm

:usedMaterial

27

)3(

3

3

3

cmV

cmV

PROBLEM

If a log has an altitude of 8m, base diameter of 0.5m. Right diameter of 0.4m. if it rolls out to the

ground covering 1 hectare of land. How many revolutions will it make?


5/13

10

4.05.0

8

:eforsolving

4.0

2.022

:Perimeter

e

e

P

rP

k

k

77.795

410000

.100001

4

104.0

:areaLateral

2

n

nm

msqhectare

L

L

ePL k

PROBLEM

A __________ of initial value or boundary value is a function y(x) which solves the differential equation

and satisfies all the subsidiary conditions.

SOLUTION

PROBLEM

It is the set of all solution in the differential equation. GENERAL SOLUTION

PROBLEM

What is the order of the differential equation?

THE HIGHEST ORDER OF THE DERIVATIVE FOUND IN THE EQUATION

PROBLEM

Evaluate the integral of ?

Solution:

ANSWER:

PROBLEM

Find the length of the arc of on [1,4].

Solution:

By Calculator: L = 7.63 units

PROBLEM

Find the volume of the solid formed by revolving the area bounded by , x =0, y = 0, about

the x-axis.

Solution:

By Calculator: V = 53.62 cu. units


6/13

PROBLEM

Find the volume of solid of revolution formed by revolving the area bounded by , x = 0, y = 2,

about the line y = 4.

Solution:

By Calculator: V = 41.88 cu. units

PROBLEM

Solve the differential equation with initial condition y(0) = 4.

Solution:

y(0) = 4 means that when x = 0, then y = 4

4 = C

ANSWER:

PROBLEMWhat kind of graph will you have when plotting r = a cos3?

3 leafed rose

PROBLEM

What kind of graph will you have when plotting r = a cos2?

4 leafed rose

PROBLEM


7/13

A salad bowl in a shape of a hemisphere has a diameter of 40 cm. If the salad occupies a height of 15

cm, determine the volume of the salad and percentage volume of the salad with respect to the volume

of the bowl.

Given: D = 40 cm

h = 15 cm

Required: (a)VS (b)%V

Solution: using Pythagorean theorem,

52+r

2=20

2

r2 = 375cm2

(a) VS =

VS = 10,602.875 cm3

(b)Vbowl =

Vbowl = 16,755.16 cm3

%V = %

%V = 63.28 %

PROBLEM

A cone with a diameter of 6 cm is inscribed in a sphere with a radius of 8 cm. Compute for the volumeand surface area of the cone.

Given: R = 8 cm

d = 6 cm

Required: (a) Vcone (b) Acone

Solution: using Pythagorean theorem,

32+h2=82

h2

= 55cm2

(a) Vcone = = 994.08 cm3

(b) Acone = R(2h+r) = 448.18 cm2

PROBLEM

A buoy is made up of a spherical segment and a cone. The angle of depreciation of the cone is 30 and

the slant side of the cone is 2 cm long. Determine the volume and surface area.


8/13

Given: = 30

R = 2 cm

Required: (a) V (b) A

Solution:

h = 2 2cos30 = 0.268 cm

sin30 =

r = 2sin30 = 1 cm

(a) V = = 2.245 cm3

(b) A = +r) = 9.65 cm2

PROBLEM

Three circles are tangent to each other inside and a big circle is tangent to them. The radius of the 3

circles is 10 cm each. Find the area of the bigger circle

cos 30 =

b=11.25

R=10+11.25

A= R2

A=1418.63

PROBLEM

Ans: cot

PROBLEM

A cylindrical smokestack in a ship has a height of 5. In an instant it fills with a 25m3

smoke. What is its

radius?

V=

R=1.26

PROBLEM


9/13

V=AL

V=

V=150,000cm3

V=150,000cm3

x

V=150 L

PROBLEM

Filled with water: height is 25 cm

=

X= 31.25

V=AL

V=

V= 58,593.75 cm3

x

V= 58.59 L

PROBLEM

Find the volume bounded by , x = 0, and y = 1 rotated along the x-axis.

V= 2

R = y V= 2

L = V= 47.88

PROBLEM

Find the volume bounded by , x=1, x=0, and y=0 rotated along the y-axis.

V= 2

R = x

L =

V= 2

V= 7.85

PROBLEM

Find the volume of the region bounded by , y=2x rotated along the x-axis.


10/13

V= 2

R = y

L =X right X left

L =

V= 2

V= 13.40 = 64

PROBLEM

Find the volume of the solid region bounded by and y=0 along x-axis.

V=

R =

V=

V= /30

PROBLEM

A force 5 pounds compresses a spring 2 inches from its original length 14 inches. Find the work done if

it compresses a total of 6 inches.

W=

F = kx

5 = k (2)

K = 5/2

W=

W = 45 in-lb

PROBLEM

At 12:00 noon, ship B is 100 miles east of ship A. Ship B sails west at 10 mi/hr and ship A sails south at

20 mi/hr. When is the two ships closest to each other?

-2000 + 200t + 800t = 0

t = 2 hrs

time = 12 noon + 2 hrs = 2:00 pm


11/13

PROBLEM

At 12:00 noon, ship B is 100 miles east of ship A. Ship B sails west at 10 mi/hr and ship A sails south at

20 mi/hr. What is the closest distance between the ships?

-2000 + 200t + 800t = 0

t = 2 hrs

z =

z =

z = 89.44 = 40 miles

PROBLEM

Find the volume of the solid formed by revolving the eq. f(x)=4-x^2, y=1,x=0 about y=1.

y=4-x^2

y-1=(4-x^2)-1

to find the limits, use the eq. and subs.y=1 to the eq. and find x.you will get 3 therefore limits are from x=0 and x=+sq.root of 3

3

0

2)3( dxxV

(hanggang jan na lang po ung natandaan ko, ndi ko na po sure ung kasunod)

Ans. 26.1 --- yan po sagot sa bookletPROBLEM

A right circular cone tank has a dimensions of 4ft @ the top and is 12 ft high. Find the work done to

pump the water 4ft above the top of the tank.

(Senxa na, mali ung sagot na lumabas dun sa computation ko kaya ndi ko na nilagay)


12/13

Ans. 43680*pi ft-lb. sagot sa booklet

PROBLEM

Find the work done to stretch a 2.5cm bar, w/ a force of F= 4, to an additional of 2cm.

F=kx4=k(2.5)

k=1.6

PROBLEM

Find the area bounded by f(x)=sine(x) and g(x)=cosine(x) and the value of x are 0


13/13

h r 2

Soln.

2 = 81.44888889

= 270(81.44888889 )

= 188.55111111

math coaching1 2ndbooklet(final)

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