I'm trying to find the volume and surface area of a curved surface which is similar to that of a banana using calculus, however I am having difficulty because normally, one would due this using a volume of revolution, but there is no straight axis through which the curves modelling the banana could be revolved. Could someone please give some suggestions as to how I could approach this?
2026-04-11 12:55:49.1775912149
Volume and Surface Area of Banana using Calculus
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You might be interested in Cavalieri's principle:
This way, if you can find the area of every slice of your banana, you can compute the volume of another banana, one which is a solid of revolution, that has the same area for each slice (so you would just integrate the area over the length).
I don't have an easy way to find the surface area, you might have to read up on surface integrals to do that.