I was afraid someone would post this specific answer. I had my doubts, but I thought the problem is too easy to get complicated. I think I was wrong about that.
Thank you, I am able to find the solution I am looking for.
Homework Statement
find the surface area of a sphere shifted R in the z direction using spherical coordinate system.
Homework Equations
$$S= \int\int \rho^2 sin(\theta) d\theta d\phi$$
$$x^2+y^2+(z-R)^2=R^2$$
The Attempt at a Solution
I tried to use the sphere equation mentioned above and...