Question

A sphere of a cone have the same radius. If the volume of the sphere is double volume of the cone, find the ratio of the height to that radius of the cone.​

Answer 1

V ( sphere ) = 4 / 3 * pi * r^3

heights in a sphere = 2 r

v ( cone ) = 1 / 3 pi r^2 h

with same height , it would be 1 / 3 pi

r^2 2r = 2 / 3 pi r^3

4 / 3 / 2 / 3 = 2

So the cone is half of the volume of the sphere