If the radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5 : 6, find the ratio of their curved surfaces.

Given:

The radii of two cylinders are in the ratio 4 : 3.

The heights of two cylinders are in the ratio 5 : 6.

The curved surface area of the cylinder = 2πrh

Ratio of curved surface area of cylinders = $\dfrac{\text{Curved surface area of the first cylinder}}{\text{Curved surface area of the second cylinder}}$

$= \dfrac{2πr$1h1}{2πr2h2}\\[1em] = \dfrac{\cancel{2π} \times 4 \times 5}{\cancel{2π} \times 3 \times 6}\\[1em] = \dfrac{20}{18}\\[1em] = \dfrac{10}{9}\\[1em]

Hence, the ratio of the curved surface areas of two cylinders is 10 : 9.