Question

A right circular cone and hemisphere have same base and volumes. Find the ratio of the height of the cone and the hemisphere.

Answer 1

Let height of cone be h.

And radius of hemisphere (r) = height of the hemisphere (H)

Volume of cone = Volume of hemisphere

\(\frac { 1 }{ 3 }\)πr²h = \(\frac { 2 }{ 3 }\)πr² × H

⇒ h = 2H

⇒ \(\frac { h }{ H }\) = \(\frac { 2 }{ 1 }\)

⇒ h : H = 2 : 1