Triple Integral moment of inertia

[Punkyc7]

set up a triple integral for the moment of inertia Iz for the region inside the sphere
x^2+y^2+z^2=4a^2 and inside the cylinder
x^2+y^2-2ax=0

so I draw my picture and convert to cylindrical coord. and i get an integral from 0 to sqrt(4a^2-r^2)
an integral from 0 to 2acostheta and an integral from 0 to 2pi

then I multiply by 2 becuase its only the top part of the volume that i set up and the integral is integrating r^3


my question is the answer says that the theta limits and goes from 0 to pi , so why is that?

 

[ideasrule]

Is theta the polar angle? If so, the polar angle can't go above 180 degrees. (If it did, it would wrap around to the other side of the sphere, and we would just use a different phi to denote that.)