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

\[\Rightarrow \frac{2}{3}\pi r^3 = 3\pi r^2 \]

\[ \Rightarrow \frac{2}{3}r = 3\]

\[ \Rightarrow r = \frac{9}{2}\]

\[ \Rightarrow d = 9 \text { units }\]

Hence, diameter of the hemisphere is equal to 9 units.