The surface of a figure circumscribed as before about a shpere is greater than four times the great circle of the sphere.

Here is the polygon of 4N sides which is a figure circumscribes the sphere with great circle of amm'a' and we know both AA' and aa' are on a straight line since both repersent the diameter of two circles which have the same center point O.
We assume R to be the radius of that circumscribed great circle.