Question:

Find the surface area of the part of the sphere $\displaystyle x^2+y^2+z^2=a^2 (a>0)$ that lies within the cylinder $\displaystyle x^2+y^2=ax$ and above the xy plane.

While solving, the region I'm concerned about is $\displaystyle [R: (x-a/2)^2+y^2\leq a^2/4]$ however my tutor change it to polar coordinate $\displaystyle [r=acos\theta,-\pi/2\leq\theta\leq\pi/2]$ why is that so?