Question

The radii of two right circular cylinders are in the ratio $2:3$ and their heights are in the ratio $5:4$. Calculate the ratio of their curved surface areas.

Answer 1

Let the radii of $2$ cylinders be $2$r and $3$r respectively and their heights be $5$h and $4$h respectively.
Let $S_1$ and $S_2$ be the curved surface areas of two cylinders.
$S_1\to$ CSA of cylinder of radius $2$r and height $5h=S_1=2\times \pi \times 2r\times 5h=20\pi rh$
$S_2\to$ CSA of cylinder with radius $3$r and height $4h=S_2=2\times \pi \times 3r\times 4h=24\pi rh$
$\therefore \frac{S_1}{S_2}=\frac{20\pi rh}{24\pi rh}=\frac{5}{6}$
$\therefore S_1:S_2=5:6$.