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
Answer:
Option B
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
Answer:
Option C
Explanation:
Volume of
the large cube = (3^{3} + 4^{3} + 5^{3}) =
216 cm^{3}.
Let the edge
of the large cube be a.
So, a^{3} =
216
=> a = 6 cm
Required
ratio = [6 × (3^{2} + 4^{2} + 5^{2})]/(6 × 6^{2})
= (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 cm^{3}
(B) 15 cm^{3}
(C) 16 cm^{3}
(D) 20 cm^{3}
Answer:
Option A
Explanation:
∴ Volume
= ^{1}/_{3} Ï€r^{2}h = ^{1}/_{3}
× Ï€ × 3^{2} ×
4 cm^{3 }= 12Ï€ cm^{3}.
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
Answer:
Option C
Explanation:
2(15 + 12) × h =
2(15 × 12)
=> h = (180/27) m = (20/3) m.
∴ Volume
= (15 × 12 × ^{20}/_{3}) m^{3} = 1200 m^{3}.
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€ m^{2}
(B) 40Ï€ m^{2}
(C) 60Ï€ m^{2}
(D) 80Ï€ m^{2}
Answer:
Option C
Explanation:
l =
10 m,
h =
8 m.
So, r = √(l^{2} - h)^{2} = √(10^{2} -
8^{2}) = 6 m.
∴ Curved
surface area = Ï€ rl = (Ï€ × 6 × 10) m^{2} = 60Ï€ m^{2}.
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
Answer:
Option B
Explanation:
1 hectare =
10,000 m^{2}
So, Area =
(1.5 × 10000) m^{2} = 15000 m^{2}.
Depth =
(5/100) m = (1/20) m.
∴
Volume = (Area × Depth) = (15000 × ^{1}/_{20}) m^{3} = 750
m^{3}.
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 m^{2}
(B) 50 m^{2}
(C) 53.5 m^{2}
(D) 55 m^{2}
Answer:
Option A
Explanation:
Area of the
wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh)
+ lb
= [2
(4 × 1.25 + 6 × 1.25) + 6 × 4] m^{2}
= 49
m^{2}
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
Answer:
Option B
Explanation:
Volume of
water displaced = (3 × 2 × 0.01) m^{3}
= 0.06 m^{3}.
∴ 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/cm^{3}, then the weight of the
pipe is:
(A) 3.6 kg
(B) 3.696 kg
(C) 36 kg
(D) 36.9 kg
Answer:
Option B
Explanation:
External
radius = 4 cm,
Internal
radius = 3 cm.
Volume of
iron = [(22/7) × {(4)^{2} - (3)^{2}} × 21] cm^{3}
= [(22/7) × 7 × 1 ×
21] cm^{3}
= 462 cm^{3}.
∴
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
Answer:
Option C
Explanation:
Number of
bricks = Volume of the wall/ Volume of 1 brick
= (800 × 600 ×
22.5) / (25 × 11.25 × 6)
= 6400
Volume and Surface Area:
Formula: Volume and Surface Area Formulas
Solved Examples: Solved Examples: Set 01
Practice Test: Practice Test: 01 Practice Test: 02
Formula: Volume and Surface Area Formulas
Solved Examples: Solved Examples: Set 01
Practice Test: Practice Test: 01 Practice Test: 02
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