Question

The volumes and the heights of a cylinder and a cone are equal. Find the ratio of the radii of their bases.

Answer 1

Let radii of bases of cylinder and cone be $r_1$ and $r_2$ and height be h.

Given, volumes are equal

$\Rightarrow \pi r_1^{2}h=\frac{1}{3}\pi r_2^{2}h$

$\Rightarrow \frac{r_1^2}{r_2^2}=\frac{1}{3}$

$\Rightarrow \frac{r_1}{r_2}=\frac{1}{\sqrt{3}}$

$\Rightarrow r_1:r_2=1:\sqrt{3}$.