Volume and Surface Areas Quiz Set 002 | Maths Aptitude Quiz Questions and Mock Test on Volume and Surface Areas Set 2 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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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?

360 kg.

362 kg.

358 kg.

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.

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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?

$4{21/46}$ m.

$5{26/45}$ m.

$3{5/16}$ m.

$7{7/48}$ 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.

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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?

12 .

14 .

10 .

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.

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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.

700 cm.

702 cm.

698 cm.

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.

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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?

28 .

30 .

26 .

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.

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