JAMB 1990 · UME · Q43

The heights of two circular cylinders are in the ratio $2 : 3$ and their base radii in the ratio $9 : 8$ . What is the ratio of their volumes?

Worked solution (try it first)

Volume of a cylinder is $\pi r^2h$ , so the ratio of volumes is (ratio of radii) $^2$ × (ratio of heights).
$\left(\frac98\right)^2 \times \frac23 = \frac{81}{64} \times \frac23$
$= \frac{162}{192}$ .
Divide top and bottom by 6: $\frac{27}{32}$ , so the ratio is $27 : 32$ , option A.