Discussion
What is the total surface area of a hemisphere of radius r?
Answer: D
A solid hemisphere has two surfaces: the curved dome and the flat circular base.
\[ \text{curved surface} = 2\pi r^{2}, \qquad \text{flat base} = \pi r^{2} \]
\[ \text{total surface area} = 2\pi r^{2} + \pi r^{2} = 3\pi r^{2} \]
The \( 2\pi r^{2} \) option is the curved surface alone - correct for a hollow bowl, but not for a solid hemisphere, which still has its flat face.
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