Question

Note Take $\mathrm{\pi }=\frac{22}{7}$, unless stated otherwise.
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

Answer 1

Let the radius of the solid hemisphere be r units.

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

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

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

$$\begin{gathered} \therefore \frac{2}{3}\mathrm{\pi }{r}^3=3\mathrm{\pi }{r}^2 \\ \Rightarrow 2r=9\mathrm{units} \end{gathered}$$
Thus, the diameter of the hemisphere is 9 units.