Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

Answer 1

Let r be the radius of the base.

and h be the height.

Here, h = r.

Now,

The ratio of their volumes will be

Volume of cone : volume of hemisphere : volume of a cylinder

`1/3pir^2 h : 2/3 pir^3 : pir^2h`

`V_1 : V_2 :V_3 = 1/3pir^3 :2/3 pir^3 :pir^3 `

Hence `V_1 :V_2 :V_3 = 1:2:3`