So the problem that I'm trying to solve is as follows:
Assume 1/8 of a sphere with radius $r$ whose center is at the origin (for example the 1/8 which is in $R^{+}$). Now two parallel planes are intersecting with this portion where their distance is $h$ (Note:$h$ < $r$) and one of the planes passes through the origin.What is the area cut off by these two planes on the 1/8 of the sphere? You may assume anything that you think is required to calculate this area, as given, my suggestion would be the angles at which the parallel planes cross xyz planes.
Obviously I'm not interested in trivial cases for example when the plane which passes through origin is one of xy, xz or zy planes.
I hope I explained everything clearly. I wish I could draw a picture for this but I don't how. Let me know if you need more clarification. Any hint or help about how to find this area is highly appreciated.