first time posting in the math section, so please excuse my disregarding forum policies that I'm not aware of. I tried to find a solution to the problem by applying my own skills, looking up calculus books, different youtube lectures etc. Found some things for the three-dimensional special case, but that wasn't particularly helpful since I don't know how to generalize the solutions to an m-dimensional setting. Anyway, here's the problem:
Suppose we are given a cone and a sphere in m-dimensional Euclidean space. The sphere is the unit-sphere centered at the origin, as is the tip of the cone. The variables are the opening angle of the cone as well as its orientation (given as a point on its central axis). The intersection of those to primitives (assuming the cone's height is sufficiently large) is a cone with an outward curved basis. I need to know the area of the curved basis part.
Is there any obvious approach that I am missing?
Your help is appreciated.