# Solve this

Question:

Note Take $\pi=\frac{22}{7}$, unless stated otherwise.

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

Solution:

Let the radius of the solid hemisphere be r units.

Numerical value of surface area of the solid hemisphere $=3 \pi r^{2}$

Numercial value of volume of the solid hemisphere $=\frac{2}{3} \pi r^{3}$

It is given that the volume and surface area of the solid hemisphere are numerically equal.

$\therefore \frac{2}{3} \pi r^{3}=3 \pi r^{2}$

$\Rightarrow 2 r=9$ units

Thus, the diameter of the hemisphere is 9 units.