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Volume and Surface Area- Aptitude Questions and Answers

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If cost of painting is Rs 12 per sq meter of surface area, how much will it cost to paint all surfaces of a solid right circular cylinder with height of 9 meters and base area of 154 sq meters?

A)

Rs. 8448


B)

Rs. 9372


C)

Rs. 1540


D)

Rs. 3180



Correct Answer :

Rs. 8448


Explanation :

Base area of cylinder = πr2 = 154
r2 = 49
Thus, radius, r = 7

Then, Total Surface Area of cylinder = 2πr(h + r) = 2π*7*(9 + 7)
= 2* 22/7 * 7 *(9 + 7)
= 704

Hence, Cost of painting = 12 * 704
= Rs 8448

If the volume of a cylinder is 2156 cubic cm and height is 14 cm, find its radius?

A)

14 cm


B)

21 cm


C)

3.5 cm


D)

7 cm



Correct Answer :

7 cm


Explanation :

h = 14 cm, r = ?
Volume = 2156 cm3
πr2h = 2156
22/7 * r2 *14 = 2156
r2 = 2156*7 / 22*14
r2 = 49
r = 7 cm

Find the curved surface area of a right circular cylinder of height 35 cm and the base radius 6 cm?

A)

1220 cm2


B)

1230 cm2


C)

1320 cm2


D)

1330 cm2



Correct Answer :

1320 cm2


Explanation :

Curved surface area of cylinder= 2πrh
= 2*π*6*35
= 2*(22/7)*6*35 (π = 22/7)
= 1320 cm2

The volume of a cuboid is 3600 m3. If its length is 25 m and its breadth and height are in the ratio 4:1 respectively , then the total surface area of the cuboid is ?

A)

1788 m3


B)

1432 m3


C)

1825 m3


D)

588 m3



Correct Answer :

1788 m3


Explanation :

volume of a cuboid, V = LBH (L=length, B = breadth, H=height).
ratio of breadth and height =3:2, let breadth=4X and height= X.
As given
3600 = 25 * 4X * X
X2 = 36
X = 6
So, breadth=24 height=6

Total Surface Area = 2(LB + BH + HL)
= 2(25*24 + 24*6 + 6*25)
= 12(25*4 + 24 + 25)
= 12(149)
= 1788

A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe?

A)

2200 square cm


B)

4400 square cm


C)

8800 square cm


D)

17600 square cm



Correct Answer :

8800 square cm


Explanation :

Radius of cylinder pipe = 1 cm

Length or height of cylinder pipe = 14 m = 1400 cm

Surface Area of cylinder pipe = 2πrh

Surface area of cylinderpipe = 2 × 22/7 × 1 × 1400

Surface Area = 8800 square cm

If the surface area of a sphere is reduced to one ninth of the area, its radius reduced to ?

A)
One-fourth

B)
One-third

C)
One-fifth

D)

One-ninth



Correct Answer :

One-third


Explanation :

Let original and new radius of the sphere are r and R respectively
Surface Area of Sphere = 4πr2

according to the question
4πr2 = 1/9 (4πR2)
r2 = R2 / 9
r = R / 3

Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is?

A)
950

B)
1000

C)
1050

D)

1100



Correct Answer :

1050


Explanation :

Volume of cylinder = πr2h = π * (35/2)2 * 32
Volume of cone = 1/3 πr2h = 1/3 * π (4/2)2 * 7

Number of persons = Volume of cylinder / Volume of cone
=(π * 35/2 * 35/2 * 32) / (1/3 * π * 4/2 * 4/2 * 7)
= 3 * 35 * 35 * 32 / 4 * 4 * 7
= 1050

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