100+ Volume and Surface Area Questions and Answers Pdf - 1

Question: 1

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be

(A) 20 cm

(B) 23 cm

(C) 25 cm

(D) 28 cm

Ans: C

Total volume of water displaced = (4 × 50) m3 = 200 m3.

Rise in water level = \$\$({200} / {40 × 20})\$\$ m = 0.25 m = 25 cm.

Question: 2

The water in a rectangular reservoir having a base 80 m by 60 m is 6.5 deep. In what time can the water be emptied by a pipe of which the cross section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km per hour?

(A) 26 hrs

(B) 32 hrs

(C) 42 hrs

(D) 52 hrs

Ans: D

Volume of water in the reservoir = (80 × 60 × 6.5) m3 = 31200 m3

Volume of water flowing out per hour = \$\$(15000 × {20} / {100} × {20} / {100})\$\$ = 600 m3.

Total time taken to empty the tank = \$\$({31200} / {600})\$\$ hrs = 52 hrs.

Question: 3

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

(A) 10

(B) 100

(C) 1000

(D) 10000

Ans: C

Number of cubes = \$\$({100 × 100 × 100} / {10 × 10 × 10})\$\$ = 1000.

Question: 4

A cuboidal block of 6 cm and 9 cm and 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be

(A) 12

(B) 24

(C) 36

(D) 48

Ans: B

Volume of block = (6 × 9 × 12)cm3 = 648 cm3.

Side of largest cube = H.C.F. of 6 cm, 9 cm, 12 cm = 3 cm.

Volume of this cube = (3 × 3 × 3) cm = 27 cm3.

∴ Number of cubes = \$\$({648} / {27})\$\$ = 24.

Question: 5

A cube of edge 20 cm is completely immersed in a rectangular vessel containing water. If the dimensions of the base of the vessel are 20 cm by 40 cm, the rise in water level will be

(A) 2

(B) 4

(C) 8

(D) 10

Ans: D

Volume increased = (20)3 cm3 = 8000 cm3.

∴ Rise in water level = \$\$({8000} / {20 × 40})\$\$ cm = 10 cm.

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