Discussion
2 cylinders have their radii into ratio 4:7. If their heights are in the ration of 21:8 then their volumes would be in what ratio?
Answer: C
Volume of a cylinder is \( \pi r^{2}h \), so form the ratio with the \( \pi \) cancelling.
\[ \frac{V_{1}}{V_{2}} = \frac{r_{1}^{2}h_{1}}{r_{2}^{2}h_{2}} = \frac{4^{2} \times 21}{7^{2} \times 8} \]
\[ = \frac{16 \times 21}{49 \times 8} = \frac{336}{392} = \frac{6}{7} \]
So the ratio is \( 6 : 7 \). The radii enter squared and the heights only to the first power - treating both alike gives \( 84 : 56 = 3 : 2 \), which is the last distractor.
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