1. make a sketch: see attachment
2. Volume of the cylinder:
3. Relation between the height h, the radius r of the base of the cylinder and the radius R of the sphere:
. Since R = 1 you'll get
Plug in this term into the equation to calculate the volume of the cylinder:
You'll get the extreme (minimum or maximum) value of if
Plug in this value into the equation to calculate rē. You'll get:
EDIT: Forgot to attach the sketch. Sorry!