Introduction

The volume of a pyramid or cone is equal to 1/3 the area of its base times its height. If a pyramid and cone have the same height and their bases have the same area, then their volumes will be the same.

In these pages you will learn why this formula works (in particular, why we must multiply by 1/3).

You will see that a triangular pyramid is 1/3 of a triangular prism. That is, a triangular prism can be split into three triangular pyramids with the same volume, so each pyramid has 1/3 the volume of its shared prism.

Then you will see that any pyramid can be split into triangular pyramids, so again the volume is 1/3 the area of its base times its height.

Finally, a cone must also have the same volume formula, because it could be made from slices of a pyramid of the same height and same cross-sectional areas. This idea is known as Cavalieri's Principle.

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