In an exercise, we are given the cylinder, $x^2+y^2=ax$ and the sphere $x^2+y^2+z^2=a^2$, and are asked to calculate the surface area of the part of the cylinder that's inside the sphere. The recommendation in the exercise is to represent this surface parametrically as $x(\theta, z)=x$ (and then I guess we can just calculate the integral), but I can't think of a way to do this. Could anyone explain to me how we can find a parametric representation of this surface?
Thanks!