Aptitude Volume and Surface Area Test Paper 4

16) The length, breadth, and height of a brick are 10 cm, 4 cm, and 3 cm, respectively. Find the surface area of the brick?

154 cm²
156 cm²
160 cm²
164 cm²

Answer: D

Explanation:

Surface area of a Cuboid = 2(lb+ bh+ hl) cm²
So,
Surface area of a brick = 2(10*4+4*3+3*10) cm²
= 2(82) cm²= 164 cm²

17) A 6 m long and 4 m wide cistern contains water up to a breadth of 1 m 25 cm. Find the total surface area of the surface immersed in water?

42 m²
49 m²
52 m²
64 m²

Answer: B

Explanation:

Area of the wet surface =
2[lb+ bh+ hl] - lb = 2 [bh+ lh] + lb
= 2[(4*1.25+6*1.25)] +6*4 = 49 m²

Solution 2:
The area of the wet surface= Area of the base + area of the two walls 2 * (4 *1.25) + area of the other two walls 2 * (6 * 1.25) cm
= 6*4 + 2 (4*1.25) + 2 (6*1.25)
= 24+ 10 + 15 = 49 m²

18) A boat of length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. What is the mass of the man?

50 Kg
60 Kg
70 Kg
80 Kg

Answer: B

Explanation:

In this type of question, first, we will calculate the volume of water displaces then we will multiply it with the density of water.
1 cm = 0.06 m
Volume of water displaced = 3*2*0.01 = 0.06 m cube
Mass of Man = Volume of water displaced * Density of water (around 1000 kg/m³)
= 0.06 * 1000 = 60 kg

19) A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on deeper side. Find the volume of the swimming pool?

Answer: C

Explanation:

Volume will be length * breadth * height,
But, in this case two heights are given so we will take average,

Apti Volume and Surface Area
12*9*2.5m³=270m³

20) The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side

Answer: C

Explanation:

We will first calculate the Surface area of the cube, and then we will calculate the quantity of paint required.
Surface area = 6a²
=6*8²=384 sq feet
16 square feet is covered by 1 kg of paint.
384 square feet will be covered by = Apti Volume and Surface Area = 24kg of paint