The ratio of the radii of the bases and the heights of two cylinders are 2 : 3 and 6 : 5 respectively. What is the ratio of their curved surface areas?

Let r₁ and r₂ be the radii and h₁ and h₂ be the heights of the two cylinders.

Accordingly, $\frac{r_1}{r_2}=\frac{2}{3} \mathrm{and} \frac{h_1}{h_2}=\frac{6}{5}$

∴ The ratio of curved surface areas of cylinders = $\frac{2\mathrm{\pi }{r}_1{h}_1}{2\mathrm{\pi }{r}_2{h}_2}$ 

$$\begin{gathered} =\left(\frac{r_1}{r_2}\right)\times \left(\frac{h_1}{h_2}\right) \\ =\frac{2}{3}\times \frac{6}{5} \\ =\frac{4}{5} \end{gathered}$$

Thus, the ratio of the curved surface areas of the two cylinders is 4 : 5.