100+ Volume Surface Area Questions for SSC Exams - 1

Question: 1

How many bullets can be made out of a cube of lead whose edge measures 22 cm, each bullet being 2 cm in diameter?

(A) 5324

(B) 2662

(C) 2541

(D) 1347

Ans: C

Number of bullets = $${Volume of the cube} /{Volume of 1 bullet}$$

                         = $$({22 × 22 × 22} / {4/3 × 22/7 × 1 × 1 × 1}) $$ = 2541.

Question: 2

A swimming bath is 24 m long and 15 m broad. When a number of men dive into the bath, the height of the water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu.m, how many men are there in the bath?

(A) 30

(B) 32

(C) 36

(D) 42

Ans: C

Volume of water displaced = $$(24 × 15 × {1}/{100})$$m3 = $${18}/{5}$$m3.

Volume of water displaced by 1 man = 0.1 m3.

∴ Number of men = $$({18/5} /{0.1})$$ = $$({18}/{5} × 10)$$ = 36.

Question: 3

Water flows into a tank 200 m × 150 m through a rectangular pipe 1.5 m × 1.25 @ 20 kmph. In what time (in minutes) will the water rise by 2 metres?

(A) 92 min

(B) 96 min

(C) 98 min

(D) 99 min

Ans: B

Volume required in the tank = (200 × 150 × 2) m3 = 60000 m3.

Length of water column flown in 1 min. = $$({20 × 1000} /{60})$$ m = $${1000}/{3}$$ m.

Volume flown per minute = $$(1.5 × 1.25 × {1000}/{3})$$ m3 = 625 m3.

∴ Required time = $$({60000} / {625})$$ min = 96 min.

Question: 4

A plot of land in the form of a rectangle has dimensions 240 m x 180 m. A drainlet 10 m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is

(A) 1.223 m

(B) 1.225 m

(C) 1.227 m

(D) 1.229 m

Ans: C

Volume of earth dug out = (240 × 180 × 0.25) m3 = 10800 m3

Let the depth of the drainlet be h metres.

Then, volume of earth dug out

= [(1260 × 200) – (240 × 180)h]m3 = (8800h) m3.

∴ 8800h = 10800 ⇒ h = $${10800}/{8800}$$ = $${27}/{22}$$ = 1.227 m.

Question: 5

Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high.

(A) 668 cm2

(B) 768 cm2

(C) 868 cm2

(D) 968 cm2

Ans: C

Volume = (16 × 14 × 7) m3 = 1568 m3.

Surface area = [2(16 × 14 + 14 × 7 + 16 × 7)]cm2 = (2 × 434) = 868 cm2.

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