Question

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

Answer 1

I am dealing with a hemisphere of radius 5 with a small hemisphere cut-out with radius 2.

What is the mathematical way to find the intervals of phi?

Answer 2

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

Answer 3

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.
\[\phi =\cos^{-1}(\frac{z}{\rho})\]