Archimedes solved this in his famous book Sphere and Cylinder in 225 BC. The result is reportedly on his tombstone.
The ratio of the volume of the radius r sphere to the cylinder radius r, height 2r is
![\frac 2 3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/s94fhy4poaapj9vf99ca8wzexqkx2dli2g.png)
The same ratio is the ratio of the surface area of the sphere to that of the cylinder (including the ends).
Answer: Last choice