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 write the values of $\frac{H}{R}$.
Solution:
Given,
Radius of the hemisphere = Radius of the cone.
Now,
Volume of the hemisphere $\frac{2}{3} \pi R^{3}$
and
Volume of the cone $\frac{1}{3} \pi R^{2} H$
Volume of the hemisphere = volume of the cone
$\frac{2}{3} \pi R^{3}=\frac{1}{3} \pi R^{2} H$
$2 R=H$
or $\frac{H}{R}=2$
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