Volume and Surface Areas Quiz Set 004

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Question 1

The ratio of surface area to the volume of a cuboids is 9 : 1, and the sum of reciprocals of two edges is 62, what is the reciprocal of the third edge?

 A

22 .

 B

24 .

 C

20 .

 D

26 .

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 $1/c = 1/2(S/V) - (1/a + 1/b)$ = $1/2(62) - 9$ = 22.


Question 2

How much water flows per hour through a pipe of radius 42 cm, if water flows at 10 km/h? Take π = 22/7.

 A

5544 cu. m.

 B

5546 cu. m.

 C

5542 cu. m.

 D

5548 cu. m.

Soln.
Ans: a

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is ${22 × 42 × 42 × 10 × 1000}/{7 × 100 × 100}$, which can easily be cancelled to get 5544 cu. m.


Question 3

What is the volume of a right cone whose cross-section is an isosceles triangle with base 18 cm and height 40 cm?

 A

1080 π sq. cm.

 B

1081 π sq. cm.

 C

1079 π sq. cm.

 D

361 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 9 cm, and height h = 40 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(9^2 × 40)$ = 1080π.


Question 4

The ratio of surface area to the volume of a cuboids is 7 : 1, and the sum of reciprocals of two edges is 44, what is the reciprocal of the third edge?

 A

15 .

 B

17 .

 C

13 .

 D

19 .

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 $1/c = 1/2(S/V) - (1/a + 1/b)$ = $1/2(44) - 7$ = 15.


Question 5

The slant height of a right conical tent of height 5 m is 13 m. What is the curved surface area?

 A

156 π sq. m.

 B

157 π sq. m.

 C

155 π sq. m.

 D

158 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = $√{13^2 - 5^2}$ = $√{169 - 25}$ = 12. The volume is π × r × l = π × 12 × 13 = 156π sq. m.


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This Blog Post/Article "Volume and Surface Areas Quiz Set 004" 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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