What is the easiest way to find phi when dealing with triple integrals in spherical coordinates?

Question

anonymous · Answer

I am dealing with a hemisphere of radius 5 with a small hemisphere cut-out with radius 2.
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What is the mathematical way to find the intervals of phi?

anonymous · Answer

0<=theta<=2pi
2<=rho<=5

agreene · Answer

I'm pretty horrible with spherical coordinates, and even worse at trying to explain anything related to them... http://www.math.montana.edu/frankw/ccp/multiworld/multipleIVP/spherical/learn.htm has some great information on it though, including the conversions for rectangular to spherical. $$\phi =\cos^{-1}(\frac{z}{\rho})$$