# Volume and Surface Areas Quiz Set 013

### Question 1

How many boxes measuring 1 m × 1m × 1 m should be dropped into a water tank 4 m × 7 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 4 × 7 × 1 cu. m. This should be equal to the volume of the boxes to be dropped. So N × 1 × 1 × 1 = 4 × 7 × 1, which gives N = 4 × 7 = 28.

### Question 2

What is the weight of a hollow cylindrical pipe 63 cm long, and having internal and external radii as 9 and 11 cm? The pipe is made of a metal of density 2 gm/cc. Take π = 22/7.

A

15840 gm.

B

15842 gm.

C

15838 gm.

D

15844 gm.

Soln.
Ans: a

The volume of the pipe is π × (112 - 92) × 63, which is \$22/7\$ × 40 × 63. Weight = vol × density = \$22/7\$ × 40 × 63 × 2 = 15840 gm.

### Question 3

What is the volume of a right cone whose cross-section is an isosceles triangle with base 10 cm and height 12 cm?

A

100 π sq. cm.

B

101 π sq. cm.

C

99 π sq. cm.

D

\$34{1/3}\$ π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 5 cm, and height h = 12 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(5^2 × 12)\$ = 100π.

### Question 4

When a weight W kg. is kept on a 7 m × 3 m boat floating over a lake, it sinks by 7 cm. What is W, if the density of water is 1000 kg/cu. m?

A

1470 kg.

B

1472 kg.

C

1468 kg.

D

1474 kg.

Soln.
Ans: a

The weight W is equal to the weight of water displaced by it. So W = \${7 × 3 × (7/100)}\$ × 1000 = 1470 kg.

### Question 5

When a weight W kg. is kept on a 4 m × 3 m boat floating over a lake, it sinks by 5 cm. What is W, if the density of water is 1000 kg/cu. m?

A

600 kg.

B

602 kg.

C

598 kg.

D

604 kg.

Soln.
Ans: a

The weight W is equal to the weight of water displaced by it. So W = \${4 × 3 × (5/100)}\$ × 1000 = 600 kg. 