Discussion
The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are
Answer: A
For cones of equal height the volume \( \tfrac{1}{3}\pi r^{2}h \) varies as \( r^{2} \), so the height cancels from the ratio.
\[ \frac{V_{1}}{V_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{3^{2}}{5^{2}} = \frac{9}{25} \]
The ratio is \( 9 : 25 \). Carrying the radii through unsquared would give \( 3 : 5 \), which is the shape of the second distractor.
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