When deciding which type of triple integral to use to compute the volume of a shape, I am stuck on whether to use spherical or cylindrical coordinates. I read that you use spherical coordinates when a shape has spherical symmetry, and you use cylindrical coordinates when a shape has rotational symmetry. What do these mean? And can a shape have both?
2026-03-27 03:44:16.1774583056
What is the difference between rotational symmetry and spherical symmetry when deciding what type of triple integral to use?
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As any rule of thumb, this rule can misfire. It is ultimately about which type of integral will end up being simpler to calculate. (Normally it happens if you can quickly eliminate at least one variable from the calculation.) If in doubt, try both. Do a few examples and build up experience.
I have actually tried to write up a more detailed answer with rules of the type "if this - do that", but have realised half-way that I would be doing you a disservice. Namely, it would make the rule complicated enough so that, in time you would use to decide whether to use cylindrical or spherical co-ordinates - you could easily try out both.