Question

A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is ______.

Options

• 21 cm

• 42 cm

• `21sqrt(7)` cm

• `2sqrt(7)` cm

Answer 1

A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is 42 cm.

Explanation:

Let radius = r and height = h.

Since r = h

Volume V = `1/3 πr^2h`   ...(Formula for cone volume)

= `1/3 πr^3`

With V = 9702 cm³ and `π = 22/7`:

`1/3 xx 22/7 xx r^3 = 9702`

⇒ `r^3 = 9702 xx 3 xx 7/22`

= 441 × 21

= 9261

⇒ r = `root(3)(9261)`

⇒ r = 21 cm

Diameter = 2r = 42 cm.