Proposed problem

Let 8x = y^{2}, z = 0 be the equations of a parabola in the (x, y) plane of ℝ^{3}. Let C be the cone of vertex in P = (0, 0, a) and generate the segments from P to the points of the parabola. Let S be the sphere of equation x^{2} + y^{2} + z^{2} − 4z = 0.

a) Calculate the surface of the portion of C inside S.

b) Calculate the surface of that portion of S inside C.