This figure examines the intersection of the sphere  and the cone .  For definiteness, set .  In this case the two surfaces intersect when .  With Plot 3D in parametric (2 variables mode) parameterize the sphere as in spherical coordinates:   with  and .  This

 choice of s will plot the sphere from its top down to the intersection with the lower part of the cone.  For the cone parameterize it as with  and  then with   and .