I am given an ellipsoid of known dimensions. I am trying to figure out what the surface area lost would be if a hole were drilled in it at a non-perpendicular angle (since obviously, if the angle is 90 degrees, area lost = area of circle).
Any advice on how I can approach this problem? The dimensions that would be provided would be the axes of the ellipsoid, the angle at which the hole is drilled, and the width/radius of the cylinder whose intersection would cause the hole.