Question

A sphere and a cone both have a radius of 10 cm, and they have the same volume. Find the height of the cone.

Answer 1

h = 40 cm

Explanation:

The volume of a sphere is given by :

`V_s=(4)/(3)\pi r^3`

The volume of a cone is given by :

`V_c=(1)/(3)\pi r^2h`

r is radius and h is height

ATQ,

A sphere and a cone both have a radius of 10 cm and they have same volume.

`V_s=V_c\\\\(4)/(3)\pi r^3=(1)/(3)\pi r^2h\\\\4r=h\\\\h=4* 10\\\\=40\ cm`

So, the height of the cone is 40 cm.