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.
Answer & explanation
Correct answer: option 3
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