Question

A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3 : 1.

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone =

And, the formula of the volume of a cylinder with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cylinder =

Now, substituting these to arrive at the ratio between the volume of a cylinder and the volume of a cone, we get

= $\frac{{\mathrm{\pi r}}^2\mathrm{h}}{{\displaystyle \frac{1}{3}}{\mathrm{\pi r}}^2\mathrm{h}}$

=

Hence it is shown that the ratio between the volumes of a cylinder and a cone with the same base radius and the same height is indeed