Question

The radii of two right circular cylinder are in the ratio $2:3$ and their height are in the ratio $5:4$. Calculate the ratio of their volumes.

Answer 1

Volume of cylinder$=\pi r^{2}h$

$\therefore \frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

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

$=\frac{4}{9}\times \frac{5}{4}$

$=\frac{5}{9}=5:9$

So, ratio of volume is $5:9$