Take the 2-minute tour ×  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.  share|improve this questi