# Volume and Surface Areas Quiz Set 018

### Question 1

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 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 30 cm and height 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 3

What is the radius of a sphere if the ratio of volume to the surface area is 3 : 5?

A

$1{4/5}$ units.

B

$3{1/2}$ units.

C

${4/7}$ units.

D

$3{3/7}$ 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 = ${9/5}$, which is same as: $1{4/5}$.

### Question 4

An iron tank 5 m × 3 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

79 cu. m.

B

81 cu. m.

C

77 cu. m.

D

83 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 × (3 × 4 + 5 × 4) + 5 × 3. The result is 79 cu. m.

### Question 5

How much water flows per hour through a pipe of radius 14 cm, if water flows at 10 km/h? Take π = 22/7.

A

616 cu. m.

B

618 cu. m.

C

614 cu. m.

D

620 cu. m.

Soln.
Ans: a

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is ${22 × 14 × 14 × 10 × 1000}/{7 × 100 × 100}$, which can easily be cancelled to get 616 cu. m.