For some personal math study I was looking at the derivation for the general pyramid volume formula ($V=\frac{1}{3}Bh$). I understand where this comes from in the case of a square-based pyramid, but I do not understand why it holds for any other pyramid with a regular polygon base. I did the square-base derivation using integration. How would I set up the integral for some general regular polygon (ex. Triangle, Octagon, etc.). Again, this isn’t for anything in particular, just an exercise I am choosing to do for fun.
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3Cavalieri's Principle, which is a precursor to Fubini's Theorem. – Rushabh Mehta Jan 01 '22 at 18:33
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1That works for any base, because any other section parallel to the base is similar to it. Hence you can repeat the same reasoning as for a square base. – Intelligenti pauca Jan 01 '22 at 18:35