If a solid sphere of radius r unit be melted to make a solid right circular cone of height r - unit , then find the radius of the base of the cone .

Explanation

The radius of the sphere = r unit
` :.` the volume of the sphere `= 4/3 pi r^(3)` cubic - unit
` :.` The volume of the sphere ` = 4/3 pir^(3)` cubic - unit
Again , the height of the cone = x unit
` :.` the volume of the cone ` = 1/3 pix^(2) r` cubic - unit
As per question ,
` 1/3 pi r^(2) r = 4/3 pir^(3) rArr x^(2) = 4r^(2) rArr x^(2) rArr x = 2r `
Hnece the radius of base of the cone is 2r unit