Volume and Surface Area Aptitude Solved Examples - ObjectiveBooks
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# Volume and Surface Area Aptitude Solved Examples

## Volume and Surface Area Aptitude Questions and Answers with Detailed Solution:

Question No. 01
A cistern of capacity 8000 liters measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 90 cm
(B) 1 dm
(C) 1 m
(D) 1.1 cm
Explanation:
Let the thickness of the bottom be x cm.
Then, [(330 - 10) × (260 - 10) × (110 - x)] = 8000 × 1000
=> 320 × 250 × (110 - x) = 8000 × 1000
=> (110 - x) = (8000 × 1000)/( 320 × 250) = 100
=> x = 10 cm = 1 dm
=> x = 10 cm = 1 dm.

Question No. 02
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
(A) 2 : 1
(B) 3 : 2
(C) 25 : 18
(D) 27 : 20
Explanation:
Volume of the large cube = (33 + 43 + 53) = 216 cm3.
Let the edge of the large cube be a.
So, a3 = 216
=> a = 6 cm
Required ratio = [6 × (32 + 42 + 52)]/(6 × 62) = (50/36) = 25 : 18

Question No. 03
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
(A) 12 cm3
(B) 15 cm3
(C) 16 cm3
(D) 20 cm3
Explanation:

Clearly, we have r = 3 cm and h = 4 cm.
Volume = 1/3 Ï€r2h = 1/3 × Ï€ × 32 × 4 cm3 = 12Ï€ cm3.

Question No. 04
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
(A) 720
(B) 900
(C) 1200
(D) 1800
Explanation:
2(15 + 12) × h = 2(15 × 12)
=> h = (180/27) m = (20/3) m.
Volume = (15 × 12 × 20/3) m3 = 1200 m3.

Question No. 05
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
(A) 30Ï€ m2
(B) 40Ï€ m2
(C) 60Ï€ m2
(D) 80Ï€ m2
Explanation:
l = 10 m,
h = 8 m.
So, r = √(l2 - h)2 = √(102 - 82) = 6 m.
∴ Curved surface area = Ï€ rl = (Ï€ × 6 × 10) m2 = 60Ï€ m2.

Question No. 06
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
(A) 75 cu. m
(B) 750 cu. m
(C) 7500 cu. m
(D) 75000 cu. m
Explanation:
1 hectare = 10,000 m2
So, Area = (1.5 × 10000) m2 = 15000 m2.
Depth = (5/100) m = (1/20) m.
Volume = (Area × Depth) = (15000 × 1/20) m3 = 750 m3.

Question No. 07
A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49 m2
(B) 50 m2
(C) 53.5 m2
(D) 55 m2
Explanation:
Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 × 1.25 + 6 × 1.25) + 6 × 4] m2
= 49 m2

Question No. 08
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
(A) 12 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
Explanation:
Volume of water displaced = (3 × 2 × 0.01) m3
= 0.06 m3.
Mass of man = Volume of water displaced × Density of water
= (0.06 × 1000) kg
= 60 kg.

Question No. 09
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
(A) 3.6 kg
(B) 3.696 kg
(C) 36 kg
(D) 36.9 kg
Explanation:
Volume of iron = [(22/7) × {(4)2 - (3)2} × 21] cm3
= [(22/7) × 7 × 1 × 21] cm3
= 462 cm3.
Weight of iron = (462 × 8) gm = 3696 gm = 3.696 kg.

Question No. 10
How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall of 8 m × 6 m × 22.5 cm?
(A) 5600
(B) 6000
(C) 6400
(D) 7200