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

Given:

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

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

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

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

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