I have four cones. The angle of each cones is 140 degree. I need to project it onto a sphere(place it ) such that, the cones cover the maximum area with minimum overlap. I initially thought that placing each cone at 90 degree would be sufficient. But this does not look to be the case. I was thinking maybe a teatrahedron, but I still dont know how to do it in terms of equations. Also, the radius of the sphere is mportant. So I guess I need an answer in terms of r, so I can plot a graph of the radius vs the angle covered to identify the optimal point. But I do not know how to proceed. Could someone please give me some pointers?
I cannot look at it in terms of volume only. The volume of a cone depends only on radius, height. Where should I factor the angle in? THe question is where on the sphere should the center of these cones be placed?