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

Given that,
A cone, hemisphere and a cylinder stand one equal bases and have the same weight
We know that

`V_"cone ": V_"hemispere" : V_"cylinder"`

⇒ `1/3πr^2h:2/3πr^3:πr^2h`

Multiplying by 3

⇒ ` π r^2 h : 2πr^3 : 3πr^2h`or

`πr^3 : 2πr^3 : 3πr^3 [∴ r=h ∵ r^2 h = r^3]`

Or 1:2:3