Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let radius of hemisphere is r.

Volume of a cone, V₁ = `1/3` πr²h

V₁ = `1/3` πr²(r)  ...[∴ h = r]

= `1/3` πr³

Volume of a hemisphere, V₂ = `2/3` πr³

Volume of cylinder, V₃ = πr²h = πr² × r = πr³  ...[∴ h = r]

V₁ : V₂ : V₃ = `1/2` πr³ : `2/3` πr³ : πr³ = 1 : 2 : 3

Hence, the ratio of their volumes is 1 : 2 : 3.