Commentary for "On the volumes of pyramids"

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Klaas van Aarsen

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Once upon a time I learned the following formula for volumes that have a flat base, a flat top, and that have those surfaces connected by a set of straight lines.

Suppose B is the area of the base, H the area of the top, and M the area halfway up.
Then the volume formula is:
$$V = \frac h 6 (B + 4M + H)$$

For instance for a pyramid or cone this is:
$$V = \frac h 6 (B + 4 \cdot \frac B 4 + 0) = \frac 1 3 B h$$