Discussion
When Jaya divided surface area of a sphere by the sphere’s volume, she got the answer as 1/18 cm. What is the radius of the sphere?
Answer: C
Form the ratio and let the \( \pi \) cancel.
\[ \frac{S}{V} = \frac{4\pi r^{2}}{\tfrac{4}{3}\pi r^{3}} = \frac{3}{r} \]
\[ \frac{3}{r} = \frac{1}{18} \quad\Longrightarrow\quad r = 54 \text{ cm} \]
The ratio has units of inverse length, which is why the answer 1/18 cm gives a radius in centimetres. Reading the relation as \( r/3 \) instead of \( 3/r \) gives 6 cm - the second distractor.
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