Aptitude Volume and Surface Area Test Paper 1
1) The surface area of a cube is 600 cm2. The length of its diagonal is
cm- cm
- 10 cm
- 10 cm
cm
cm
cm
Answer: C
Explanation:
Surface area of cube = 6 a2
600 = 6 a2
a2 = 100
a= 
=10 cm
Diagonal of cube = 
a = × 10 = 10 cm
2) The length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high, is
- 30 m
- 15 m
- 30 m
- 60 m
Answer: C
Explanation:
Length of room = 30 m
Breadth of room = 24 m
Height of room = 18 m
3) The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.
- 150
- 140
- 120
- 100
Answer: D
Explanation:
Length of the hall = 40 m
Breadth of hall= 25 m
Height of hall = 20 m
Volume of the hall = l x b x h
= 40 x 25 x 20 = 20,000 m3
Space occupied by each person = 200m3
Number of person that can accommodate in the hall =
4) 4 cubes each of 6 cm2 total surface area and another cube of 24 cm2 total surface area are placed together in such a way to form a rectangular parallelepiped. The total surface area of the parallelepiped so formed is
- 48 cm2
- 40 cm2
- 36 cm2
- 32 cm2
Answer: A
Explanation:
Total surface area of parallelepiped = total surface area of 4 cubes + Surface area of another cube
So, the required surface area = 4 x6 + 24 = 48 cm2
5) A water tank is 30 m long, 20 m wide and 12 m deep. It is made of iron sheet which is 3 m wide. The tank is open at the top. If the cost of iron sheet is Rs. 10 per meter, what is the total cost of iron sheet required to build the tank?
- Rs. 6000
- Rs. 8000
- Rs. 9000
- Rs. 10,000
Answer: A
Explanation:
Length of water tank = 30 m
Width of water tank = 20 m
Depth of water tank = 12 m
Area of water tank = 2(lb+bh +hl) – lb
= 2 (30 x 20 + 20 x 12 + 12 x 30) – 30 x 20
= 2 (600 + 240 + 360) – 600
= 2 (1200) – 600
= 2400 – 600 = 1800 m2
Area of iron sheet (L*B) = area of tank = 1800 m2
L * B = 1800
L x 3 = 1800
L = 1800/3 = 600 m
Given that, the cost of iron sheet is Rs. 10 per meter.
So, the total cost of iron sheet to build the tank = 10 x 600 = Rs. 6000
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