Discussion
If the radius of a sphere is doubled, then what is the ratio of their surface area?
Answer: C
Surface area of a sphere is \( 4\pi r^{2} \), so it scales with the square of the radius.
\[ \frac{S_{1}}{S_{2}} = \frac{4\pi r^{2}}{4\pi (2r)^{2}} = \frac{r^{2}}{4r^{2}} = \frac{1}{4} \]
So the ratio is \( 1 : 4 \). Doubling a length quadruples an area and multiplies a volume by eight - here the volumes would be in the ratio \( 1 : 8 \).
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