Volume and Surface Areas Quiz Set 012

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Question 1

The slant height of a right conical tent of height 3 m is 5 m. What is the curved surface area?

 A

20 π sq. m.

 B

21 π sq. m.

 C

19 π sq. m.

 D

22 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = $√{5^2 - 3^2}$ = $√{25 - 9}$ = 4. The volume is π × r × l = π × 4 × 5 = 20π sq. m.


Question 2

An iron tank 4 m × 4 m is filled with water upto a height of 4 m. What surface area of the tank is at a higher risk of corrosion?

 A

80 cu. m.

 B

82 cu. m.

 C

78 cu. m.

 D

84 cu. m.

Soln.
Ans: a

If L, B and H are the dimensions of the water column, then the wet area is 2(BH + LH) + LB = 2 × (4 × 4 + 4 × 4) + 4 × 4. The result is 80 cu. m.


Question 3

What is the volume of a cone generated by rotating a right angled triangle with sides 17, 15 and 8 cm? The rotation is done about the side of length 8 cm.

 A

600 π sq. cm.

 B

601 π sq. cm.

 C

599 π sq. cm.

 D

201 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 15 cm, and height h = 8 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(15^2 × 8)$ = 600π.


Question 4

The ratio of surface area to the volume of a cuboids is 16 : 1, and the sum of reciprocals of two edges is 52, what is the reciprocal of the third edge?

 A

10 .

 B

12 .

 C

8 .

 D

14 .

Soln.
Ans: a

The well-known relation for a cuboids is $1/V = 2/S(1/a + 1/b + 1/c)$, which can be re-arranged to get $1/c = 1/2(S/V) - (1/a + 1/b)$ = $1/2(52) - 16$ = 10.


Question 5

When a weight W kg. is kept on a 4 m × 9 m boat floating over a lake, it sinks by 3 cm. What is W, if the density of water is 1000 kg/cu. m?

 A

1080 kg.

 B

1082 kg.

 C

1078 kg.

 D

1084 kg.

Soln.
Ans: a

The weight W is equal to the weight of water displaced by it. So W = ${4 × 9 × (3/100)}$ × 1000 = 1080 kg.


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This Blog Post/Article "Volume and Surface Areas Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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