Question

The radius and height of a cone and a cylinder are equal. If the volume of the cylinder is $258c{m}^3$, then the volume of the cone is ____ $c{m}^3$.

Answer 1

Let $r$ and $h$ be the radius and height of the cylinder.

Therefore,

Radius of cone $=r$

Hight of cone $=h$.

Now,

Volume of cylinder $=\pi r^{2}h=258{cm}^3$.

$⟹$ $r^{2}h=\frac{258}{\pi }$.

Now,

Volume of cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \pi \times \frac{258}{\pi }=\frac{258}{3}=86{cm}^3$.

Hence, $86$ is the answer.