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