Two circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of two radii.

Let, r1, r2 be the radii of the cylinder

h1, h2 be the height of the cylinder

v1, v2 be the volume of the cylinder

h1/h2 = 1/2 and v1 = v2

$\Rightarrow \mathrm{v}_{1} / \mathrm{v}_{2}=\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)^{2} *\left(\mathrm{~h}_{1} / \mathrm{h}_{2}\right)$

Since, v1 = v2

$\Rightarrow \mathrm{v}_{1} / \mathrm{v}_{1}=\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)^{2} *(1 / 2)$

$\Rightarrow\left(r_{1} / r_{2}\right)^{2}=(2 / 1)$

$\Rightarrow\left(\frac{r_{1}}{r_{2}}\right)=\frac{\sqrt{2}}{1}$

Hence, the ratio of the radii are √2:1