# Volume and Surface Areas Quiz Set 001

### Question 1

What is the radius of a sphere if the ratio of volume to the surface area is 2 : 31?

A

${6/31}$ units.

B

$1{7/30}$ units.

C

$2{2/33}$ units.

D

3 units.

Soln.
Ans: a

Let R be the radius. Then $V/S = {4/3 × \text"π" × R^3}/{4 × \text"π" × R^2}$ = $R/3$, so R = 3 × ratio = ${6/31}$.

### Question 2

An iron tank 5 m × 2 m is filled with water upto a height of 7 m. What surface area of the tank is at a higher risk of corrosion?

A

108 cu. m.

B

110 cu. m.

C

106 cu. m.

D

112 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 × (2 × 7 + 5 × 7) + 5 × 2. The result is 108 cu. m.

### Question 3

What is the length of a 10 mm wire that has been drawn out of a lump of 11 cu. cm. tin? Take π = 22/7.

A

350 cm.

B

352 cm.

C

348 cm.

D

354 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 ${1/10} × {1/10} × L$ = 11, which gives L = ${10 × 10 × 11 × 7}/22$ = 350 cm.

### Question 4

A cone of height 8 cm and radius of base 16 cm is made up of modeling clay. A child reshapes it in the form of a sphere. What is the radius of the sphere?

A

8 cm.

B

10 cm.

C

6 cm.

D

12 cm.

Soln.
Ans: a

Let the radius of the sphere be R. The volumes are equal. So $4/3$ π R3 = $1/3$ π 162 × 8. Cancelling π/3 from both sides, R3 = ${16 × 16 × 8}/4$ = 512 = 83. So R = 8 cm.

### Question 5

The ratio of surface area to the volume of a cuboids is 9 : 1, and the sum of reciprocals of two edges is 74, what is the reciprocal of the third edge?

A

28 .

B

30 .

C

26 .

D

32 .

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 $1/c = 1/2(S/V) - (1/a + 1/b)$ = $1/2(74) - 9$ = 28.