Question

A copper sphere of radius 3cm is melted and recast into a right circular cone of height 3cm.find radius of base of cone?

Answer 1

Given radius of sphere = 3cm

Volume of a sphere =`4/3pir^3`

`=4/3xxpixx3^3cm^3`         .........(1)

Given sphere is melted and recast into a right circular cone

Given height of circular cone = 3cm.

Volume of right circular cone `=pir^2xx1/3`

`=pi/3(r)^2xx3cm^2`       ..........(2)

Equating 1 and 2 we get

`4/3pixx3^3=1/3pi(r)^2xx3`

`r^2=(4/3pixx3^3)/pi`

r² = 36cm

r = 6cm

∴ Radius of base of cone(r) = 6cm