Question

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then.

• A. $H=2R$
• B. $H=3R$
• C. $H=\sqrt{3}$R
• D. $H=\frac{2}{3}$R

Answer 1

The correct option is A $H=2R$

Radius of Hemisphere $=R$

Volume of Hemisphere $=\frac{2}{3}\pi R^3$

This Hemisphere is recasted into a Cone,

$\Rightarrow$ Volume remains same.

Therefore, $\frac{2}{3}\pi R^3=\frac{1}{3}\pi R^{2}H$

Here $H$ is Height of the Cone

$\Rightarrow H=2R$