# Volume and Surface Areas Quiz Set 012

### Question 1

The slant height of a right conical tent of height 3 m is 5 m. What is the curved surface area?

A

20 π sq. m.

B

21 π sq. m.

C

19 π sq. m.

D

22 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = \$√{5^2 - 3^2}\$ = \$√{25 - 9}\$ = 4. The volume is π × r × l = π × 4 × 5 = 20π sq. m.

### Question 2

An iron tank 4 m × 4 m is filled with water upto a height of 4 m. What surface area of the tank is at a higher risk of corrosion?

A

80 cu. m.

B

82 cu. m.

C

78 cu. m.

D

84 cu. m.

Soln.
Ans: a

If L, B and H are the dimensions of the water column, then the wet area is 2(BH + LH) + LB = 2 × (4 × 4 + 4 × 4) + 4 × 4. The result is 80 cu. m.

### Question 3

What is the volume of a cone generated by rotating a right angled triangle with sides 17, 15 and 8 cm? The rotation is done about the side of length 8 cm.

A

600 π sq. cm.

B

601 π sq. cm.

C

599 π sq. cm.

D

201 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 15 cm, and height h = 8 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(15^2 × 8)\$ = 600π.

### Question 4

The ratio of surface area to the volume of a cuboids is 16 : 1, and the sum of reciprocals of two edges is 52, what is the reciprocal of the third edge?

A

10 .

B

12 .

C

8 .

D

14 .

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(52) - 16\$ = 10.

### Question 5

When a weight W kg. is kept on a 4 m × 9 m boat floating over a lake, it sinks by 3 cm. What is W, if the density of water is 1000 kg/cu. m?

A

1080 kg.

B

1082 kg.

C

1078 kg.

D

1084 kg.

Soln.
Ans: a

The weight W is equal to the weight of water displaced by it. So W = \${4 × 9 × (3/100)}\$ × 1000 = 1080 kg. 