Question

The ratio of radii of two cylinders is $1:2$ and heights are in the ratio $2:3.$ The ratio of their volumes is

Answer 1

Let $V_1$ be the volume of 1st cylinder and $V_2$ be the volume of 2nd cylinder

$V_1=\pi r_1^2{h}_1$

$V_2=\pi r_2^2{h}_2$

$\Rightarrow \frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^2\frac{h_1}{h_2}$

$={\left(\frac{1}{2}\right)}^2\times \frac{2}{3}$

$=\frac{1}{4}\times \frac{2}{3}$

$=\frac{1}{6}$