Find the surface area of the part of the sphere $x^2 + y^2 + z^2 = a^2$ inside the circular cylinder $x^2 + y^2 = ay$ ($r = a\sin(\theta)$ in polar coordinates), with $a > 0$.
First time posting on this website, sorry for the lack of details on my attempts but I am really not sure where to start on this problem.
A formula that is useful is $ \displaystyle A(G) = \iint \sqrt{f_x^2 + f_y^2 + 1} \, dA.$
$f_x$ is the partial derivative with respect to $x,$ $f_y$ is the partial derivative with respect to $y$
I know that I need to find an equation which should be $x^2 + y^2 + z^2 = a^2$, and I need to find the limits which is where I am really struggling.
Also according to my professor, I shouldn't have to use any polar coordinate conversions in order to complete this problem, which was my initial approach.