Question

The radii of two cylinders are in the ratio $2:3$ and their heights are in the ratio $5:3$. Calculate the ratio of their volumes and the ratio of their curved surfaces.

Answer 1

Let the radii be $r_1=2x$ and $r_2=3x$. Height be $h_1=5y$ and $h_2=3y$. Then,
$\frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}=\frac{4x^2\times 5y}{9x^2\times 3y}=\frac{20}{27}$
and $\frac{S_1}{S_2}=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}=\frac{10xy}{9xy}=\frac{10}{9}$.