Discussion
If radii of two cylinders are in the ratio 5 : 3 and their heights are in the ratio 3 : 5 then ratio of their volumes is
Answer: D
The ratio of the volumes is 5 : 3.
The volume of a cylinder is \(\pi r^{2} h\), so the ratio of volumes is the square of the radius ratio times the height ratio:
\[ \begin{aligned} \frac{V_{1}}{V_{2}} &= \left(\frac{5}{3}\right)^{2} \times \frac{3}{5} \\ &= \frac{25}{9} \times \frac{3}{5} = \frac{5}{3} \end{aligned} \]
9 : 25 is the squared radius ratio upside down, and 5 : 5 or 3 : 3 (that is 1 : 1) is what you get by forgetting to square the radii.
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