A hemisphere, a cone and a cylinder stand on equal bases and their respective heights are in the ratio 1 : 2 : 3. Find the ratio of their volumes.

2 : 2 : 9

Volume of hemisphere = \(\frac{2}{3}\) πr³

Volume of cone = \(\frac{1}{3}\) πr²h 

Volume of cylinder = πr²h

Ratio of height of hemisphere, a cone and a cylinder = 1 : 2 : 3

Ratio of volume of hemisphere, a cone and a cylinder

= \(\frac{2}{3}\) πr³ : \(\frac{1}{3}\) πr²h : πr²h 

= 2× 1 : 2 : 3 × 3

= 2 : 2 : 9

The correct answer is option (3) : 2 : 2 : 9