Question

If a cone, a hemisphere and a cylinder have equal bases and have equal heights, then the ratio of their volumes is ______.

Options

• 2:3:1

• 1:2:3

• 3:2:1

• 2:1:3

Answer 1

If a cone, a hemisphere and a cylinder have equal bases and have equal heights, then the ratio of their volumes is 1:2:3.

Explanation:

Since the shapes have equal bases and equal heights, their radius is r and height is h = r (as the height of a hemisphere equals its radius)

The ratio of their volumes is:

Cone : Hemisphere : Cylinder = `1/3πr^2 h : 2/3 πr^3 : πr^2 h` 

Substituting h = r, this simplifies to:

`1/3 πr^3 : 2/3 πr^3 : πr^3`

= `1/3 : 2/3 1`

= 1:2:3