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).

Answer 1

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