Discussion
The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
Answer: C
Area varies as the square of the radius, so the ratio is squared.
\[ \frac{A_{1}}{A_{2}} = \frac{\pi r_{1}^{2}}{\pi r_{2}^{2}} = \left(\frac{1}{3}\right)^{2} = \frac{1}{9} \]
So the areas are in the ratio \( 1 : 9 \). Carrying the linear ratio straight through gives \( 1 : 3 \) - the circumferences, not the areas.
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