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How do we know when to use spherical coordinates and when to use cylindrical coordinates? What do we base it on, the surface or the equation of the function we are given?

e.g in a question I'm given $z^{2}=x^{2}+y^{2}+1,z>0$ and $x^{2}+y^{2}+z^{2}=3$. I thought we should use spherical coordinates but we have to use cylindrical so clearly there should be a way to determine when to use which.

Shevliaskovic
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user134785
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  • There is something strange here. If $x^2 + y^2 + z^2 = 3$, then $z^2 = 3 - x^2 - y^2$. If you are also given that $z^2 = 1 + x^2 + y^2$, then $3 - x^2 - y^2 = 1 + x^2 + y^2$, which means that $x^2 + y^2 = 1$. These facts and the fact $z > 0$ imply that $z = 2$. Where's the surface? – David K May 05 '14 at 12:28

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