Can anyone help me, I need to calculate the area surface area removed from a spherical surface when a rectangular cut is made in it? The geometry is somewhat similar to pic related, however a 2d projection of the rectangle taken normal to the sphere from the center of the rectangle would produce a true rectangle(all opposite sides are parallel). So my equation would be sa=r^2*dTheta*dPhi. However, the rectangle has rounded corners, just arcs tangent to the two edges, and this is what i cannot account for. Can any one help me please?