1. ## Finding Mass

I am having trouble with the following question:

Find the mass of a ball B given by (x^2) + (y^2) + (z^2) <= (a^2) if the density at any point is proportional to its distance from the z-axis.

Any ideas or help would be appreciated. Thanks!

2. You need to change variables. Rectangular is painful. The density here is
$kr=k\sqrt{x^2+y^2}=k\rho\sin\phi$, but the k's cancel, so you can let k=1.
Try spherical, where the Jacobian is $\rho^2\sin\phi$.
If you're integating over the entire ball, then $0<\rho , $0<\theta <2\pi$ and $0<\phi<\pi$.