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I'm interested to know if anyone can point me to a non-calculus way of seeing that the $\text{volume of a pyramid} = \frac{1}{3}\times(\text{area of base})\times(\text{height})$. Yes, I've googled.

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    There are many kinds of pyramids. Do you have any particular type in mind? For example, one might take a convex n-gon and take the convex hull with a point that does not lie in the plane of the n-gon.2010-11-04
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    @Joseph: He meant the one with a square base I suppose.2010-11-04

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