# Volume and Surface Areas Quiz Set 002

### Question 1

When a weight W kg. is kept on a 6 m × 3 m boat floating over a lake, it sinks by 2 cm. What is W, if the density of water is 1000 kg/cu. m?

A

360 kg.

B

362 kg.

C

358 kg.

D

364 kg.

Soln.
Ans: a

The weight W is equal to the weight of water displaced by it. So W = \${6 × 3 × (2/100)}\$ × 1000 = 360 kg.

### Question 2

A room has a floor size of 5 × 41 sq. m. What is the height of the room if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

A

\$4{21/46}\$ m.

B

\$5{26/45}\$ m.

C

\$3{5/16}\$ m.

D

\$7{7/48}\$ m.

Soln.
Ans: a

Let h be the height, and l and b be the length and breadth. We are given lb + lb = lh + hb + lh + hb. Combining the terms and cancelling 2, we get lb = h(l + b), which gives h = \${lb}/{l + b}\$ = \${5 × 41}/{5 + 41}\$ = \${205/46}\$, which is same as: \$4{21/46}\$ m.

### Question 3

The ratio of surface area to the volume of a cuboids is 5 : 1, and the sum of reciprocals of two edges is 34, what is the reciprocal of the third edge?

A

12 .

B

14 .

C

10 .

D

16 .

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(34) - 5\$ = 12.

### Question 4

What is the length of a 10 mm wire that has been drawn out of a lump of 22 cu. cm. tin? Take π = 22/7.

A

700 cm.

B

702 cm.

C

698 cm.

D

704 cm.

Soln.
Ans: a

The wire is a cylinder with r = 1/10 cm, and length L. The volume of tin is equal to the volume of the wire. So π \${1/10} × {1/10} × L\$ = 22, which gives L = \${10 × 10 × 22 × 7}/22\$ = 700 cm.

### Question 5

How many boxes measuring 1 m × 1m × 1 m should be dropped into a water tank 7 m × 4 m so that the water level rises by 1 m?

A

28 .

B

30 .

C

26 .

D

32 .

Soln.
Ans: a

The volume of water to be displaced is 7 × 4 × 1 cu. m. This should be equal to the volume of the boxes to be dropped. So N × 1 × 1 × 1 = 7 × 4 × 1, which gives N = 7 × 4 = 28.

This Blog Post/Article "Volume and Surface Areas Quiz Set 002" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-11

Posted by Parveen(Hoven),
Aptitude Trainer