Show that the surface area of a sphere is two-thirds of the total surface area of any cylinder circumscribed around the sphere (the sphere, therefore, touches both bases of the cylinder as well as its lateral surface).
the sphere and cylinder have the same radius
the cylinder's height is the diameter of the sphere, or twice its radius.
sphere has area 4πr^2
cylinder has area 2πr^2 + 2πr(2r) = 6πr^2