Question

__________ times the volume of a cone is equal to the volume of a cylinder having height and radius same as that of the cone.

Answer 1

Find the number of times the volume of a cone is equal to the volume of a cylinder.

Let the number of times be $n$

Given that, the radius of the cone $=$ radius of the cylinder $=r$

And, the height of the cone $=$ height of the cylinder $=h$

The volume of the cone of radius $r$ and height $h$$=\frac{1}{3}\pi r^{2}h$

The volume of the cylinder of radius $r$ and height $h$$=\pi r^{2}h$

We have, $n\times Volumeofthecone=Volumeofthecylinder$

$$\begin{gathered} \therefore n\times \frac{1}{3}\pi r^{2}h=\pi r^{2}h \\ \Rightarrow n=3 \end{gathered}$$

Therefore, the required number is three.

Hence, three times the volume of a cone is equal to the volume of a cylinder having height and radius same as that of the cone.