Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?

Answer 1

Let r be the radius of the base.

And h is 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 : 2/3pir^3 : pir^2 h `

`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`