Question

Two circular cylinders of equal volume have their heights in the ratio $1:2$ The ratio of their radii is

Answer 1

Finding the ratio of their radii:

Let the height be $h$ and $2h$ and radii are$r$ and$R.$

$$\begin{gathered} \frac{{\mathrm{\pi r}}^2\mathrm{h}}{{\mathrm{\pi R}}^2\mathrm{h}}=\frac{2}{1} \\ \frac{r^2}{R^2}=\frac{2}{1} \\ \frac{r}{R}=\sqrt{\frac{2}{1}} \\ \frac{r}{R}=\frac{\sqrt{2}}{1} \\ \therefore r:R=\sqrt{2}:1 \end{gathered}$$
Therefore the ratio of their radii become $r:R=\sqrt{2}:1$