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Volume is defined in terms of limits, so there's no hope to prove this without taking a limit of some form. Whether or not you count that as calculus is up to y
by OscarCunningham 3y ago
Volume is defined in terms of limits, so there's no hope to prove this without taking a limit of some form. Whether or not you count that as calculus is up to you.
- walnutclosefarm 3y agoI don't know that limit is the key factor here, but I agree on the calculus part. The arguments that rely on Cavalieri's principle to relate the volume of the cone to the volume of a slice-by-slice identical pyramid, for example, don't really involve a limit per se, but they are clearly motivational for integral calculus. Basically every intuitional argument for this, and other volume formulas, are somewhere on the road to integral calculus.