Discussion
A sphere with surface area \( \dfrac{792}{7} \) sq. cm has a volume of ____
Answer: C
Find the radius from the surface area first, taking \( \pi = \tfrac{22}{7} \).
\[ 4\pi r^{2} = \frac{792}{7} \quad\Longrightarrow\quad r^{2} = \frac{792}{7} \times \frac{7}{4 \times 22} = \frac{792}{88} = 9 \]
\[ r = 3 \text{ cm} \]
\[ V = \frac{4}{3}\pi r^{3} = \frac{4}{3} \times \frac{22}{7} \times 27 = \frac{792}{7} \text{ cm}^{3} \]
The numerical coincidence is real, not a misprint: for \( r = 3 \) the surface area and volume come out to the same number, because \( \tfrac{V}{S} = \tfrac{r}{3} = 1 \).
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