Question

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

Answer 1

Let the radius of the hemisphere be r units.
Volume of a hemisphere = Surface area of the hemisphere
$$\begin{gathered} \Rightarrow \frac{2}{3}\mathrm{\pi }{r}^3=3\mathrm{\pi }{r}^2 \\ \Rightarrow \frac{2}{3}r=3 \\ \Rightarrow r=\frac{9}{2} \\ \Rightarrow d=9\mathrm{units} \end{gathered}$$
Hence, diameter of the hemisphere is equal to 9 units.