Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.
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When dealing with ratios of volumes or areas of similar geometric shapes, express the ratio of the formula variables and then substitute the given ratios. For example, for cones, $V \propto r^2h$, so $\frac{V_1}{V_2} = \left(\frac{r_1}{r_2}\right)^2 \left(\frac{h_1}{h_2}\right)$.