#### 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.

#### Solution

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

Is there an error in this question or solution?

Solution 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. Concept: Volume of a Sphere.