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

cylinder: 2πrh+2πr^2
sphere: 4πr^2

Now, since h=2r,

4πr^2 / 2πr*2r+2πr^2 = 4πr^2 / 6πr^2 = 2/3