Use a triple integral in spherical coordinates to ﬁnd the volume, $V$, of a cored apple, which consists of a sphere of radius $2$, $x^2 + y^2 + z^2 = 4$, and a cylindrical hole of radius one, $x^2 + y^2 = 1$. In other words, ﬁnd the volume of the sphere with the cylinder removed.
I know that $\theta$ goes from $0$ to $2\pi$ since the sphere is complete. What I don't understand is how to:
1) Convert rectangular coordinates to spherical coordinates. My textbook gives a terrible explanation.
2) Find the bounds of the triple integral. As I said, $\theta$ goes from $0$ to $2\pi$. I have no clue as to how to find $p$ or $\varphi$. The center being removed is also throwing me.
Could some explain as to how to go about this? I'm not necessarily looking for answer but a means to solve this problem. We have an exam next week and I would really love to be able to understand it.