If a V-shaped cut were to be made through an entire sphere, radius DR (Dome Radius) with a Cutting Angle (CA- angle of the cut), what would be the surface area of the sphere section that would be cut? This is assuming that CA is less than 180 degrees. Also the Cut Depth (CD- depth of the V-shaped cut from the top of the sphere to the bottom of the "V") is to be less than the Dome Radius (DR). So, the Area of the cut-out section (A) would be in terms of DR, CA, and CD. Any help in figuring out this problem would be greatly appreciated! If CD were to be equal to DR, this problem would not be too difficult, because the shape of the cut-out section would be a "loon," but since CD must be less than DR, it is quite tougher. I don't think that spherical triangles could be used either because since CD is not equal to DR, the circles that would cut out the section would not be Great Circles (not straight lines, but curved lines I believe) so this adds a great deal of difficulty to the problem.