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

 Given:

A cylinder and a cone have equal radii of their bases and equal heights.

To do:

We have to show that their volumes are in the ratio $3:1$.

Solution:

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

Therefore,

Volume of the cylinder $= \pi r^2h$

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

Ratio of the volumes of the cylinder and the cone $=\pi r^{2} h: \frac{1}{3} \pi r^{2} h$

$=1: \frac{1}{3}$

$=3: 1$

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Updated on: 10-Oct-2022

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