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.

Answer 1

Ratio of radii of two cylinders $=2:3$

and the ratio of heights $=5:3$

Let $r_1,h_1$ and $r_2,h_2$ be the radii and heights of two cylinders respectively.

$\therefore \frac{r_1}{r_2}=\frac{2}{3}$ and $\frac{h_1}{h_2}=\frac{5}{3}$

Now $\frac{\text{Volume~of~first~cylinder}}{\text{Volume~ of~second~cylinder}}=\frac{\pi (r_1{)}^2{h}_1}{\pi (r_2{)}^2{h}_2}$

$={\left(\frac{r_1}{r_2}\right)}^2\times \left(\frac{h_1}{h_2}\right)$

$={\left(\frac{2}{3}\right)}^2\times \frac{5}{3}$

$=\frac{4}{9}\times \frac{5}{3}=\frac{20}{27}$