HOW is the "shape" given? Do you know a formula in Cartesian coordinates? No one can tell you how to find without knowing what you are given! Also, there is no single " " for a surface. There is a for each point on the surface.
I am having trouble doing problems in spherical coordinates, specifically, finding phi. I know it's the angle between the z axis and the shape but I don't know a good strategy for finding that especially on a cone. What are easy ways to do this?