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.