Question

A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. Find the radius of the base of the cone.

Answer 1

Radius of hemisphere = 9 cm

Volume of hemisphere = `2/3pir^3= 2/3pixx9xx9xx9   "cm"^3`

Height of cone = 72 cm

Let the radius of the cone be r cm.

Volume of the cone `= 1/3pir^2h=1/3pir^2xx 72  "cm"^3`

The Volume of the hemisphere and cone are equal.

Therefore,

`1/3pir^2xx72xx =2/3xx9xx9xx9xx9`

`r^2 =(2xx9xx9xx9)/72 = 81/4`

`r = sqrt(81/4) = 9/2 = 4.5  "cm"` 

The radius of the base of the cone is 4.5 cm.