Volume and Surface Area- Aptitude Questions and Answers

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A hall is 12m long and 8m broad. If the sum of the area of the floor and the ceiling is equal to the sum of the area of the four walls. Find the height of the hall (in m)

A)
4.8

B)
6.4

C)
8.3

D)
3.2


Correct Answer :

4.8


Explanation :

Area of 4 walls of a room = (l*h)+(b*h)+(l*h)+(b*h) =2(l*h)+2(b*h) = 2h(l+b)
Area of the floor + Area of ceiling =>(l*b) +(l*b) => 2*(l*b)

We have,
Area of 4 walls of a room= Area of the floor + Area of ceiling
Hence,
2 * h*(12 + 8) = 2*(12 * 8)
h = 96/20 = 4.8 m

If each side of a cube is 3 centimeter,then its surface area is :

A)

54 Cubic Centimeter


B)

9 Square Centimeter


C)

54 Square Centimeter


D)

None of these



Correct Answer :

54 Square Centimeter


Explanation :

if side of the square as “a”, then
Surface area of a cube = 6a2 = 6*(3)2 = 54 cm2

A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to the smaller cubes?

A)

1/6


B)

1/5


C)

1/25


D)

1/125



Correct Answer :

1/5


Explanation :

The volume of the original cube = 53 = 125 cm3.
The volume of a smaller cubes = 13 = 1 cm3.
Therefore, we will be get total smaller cubes = 125/1 = 125

The surface area of the larger cube = 6*a2 = 6(52) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.

Hence, the required ratio = 150 / 750 = 1 / 5

If the surface area of sphere is 346.5 cm2, then its radius is [ taking π=22/7 ]?

A)

5.25 cm


B)

7.25 cm


C)

3.25 cm


D)

9.25 cm



Correct Answer :

5.25 cm


Explanation :

Surface area of sphere= 4πr2
4 * 22/7 * r2 = 346.5
r2 = 346.5 * 7 / 4 * 22 = 27.5625
r = √27.5625 = 5.25 cm

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

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