Question

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.

Answer 1

Radius of hemisphere r = 7 cm

The volume of hemisphere

`= 2/3 pir^3`

`=2/3 pi xx (7)^3`

`= 2/3 pi xx 343`

`= (686)/3 pi cm^3`

Since, the hemisphere cast into the right circular cone

The height of cone h = 49 cm

Let x be the radius of cone.

Clearly,

Volume of cone = volume of hemisphere

`1/3 pi xx 49 = (686)/3 pi`

            `x^2 = (686 xx 3)/(49 xx 3)`

                `= 14`

`x^2 = 14`

`x = sqrt4`

`x = 3.74 cm`

Thus, the radius of cone = 3.74 cm