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Ok, so a cube and a sphere are both centered at origo. The cube has side lengths L. I need to know the surface area of the part of the sphere that is inside the cube, for all possible r. There will be three different equations, one for [itex]0 < r < L/2[/itex], when the entire sphere is inside the cube, one for [itex]L/2 < r < L/\sqrt(2)[/itex], when six spherical caps of the sphere stick out of the cube sides , and one for [itex]L/\sqrt(2) < r < L\sqrt(3) / 2[/itex], when only the corners of the cube is visible. I have figured out the two first, but not the last.
Any help would be greatly appreciated!
Any help would be greatly appreciated!