Let P_n be a sequence of polyhedrons inscribed into unit sphere or radius 1, such that maximum size s of all its faces tends to zero s \rightarrow 0. Size of the face is maximum distance between any two points of the face.

Prove that limit of surface areas S of polyhedrons is 4 \pi, that is

 \lim_{s \rightarrow 0} S(P) = 4 \pi