OK. The reason I did not show my work is because i believe there must be a much simpler way. But her it is.
If I am not mistaking, the area X of the sphere INSIDE the cube is the total area A of the sphere, minus the area C of the six spherical caps, plus the area of the overlaps E between...
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 0 < r < L/2, when the entire sphere is inside the cube, one...