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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.

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Solution

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

= πr2h13πr2h

=

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


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