A right circular cone and hemisphere have same base and volumes. Find

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

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

Answer»

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