<s>[INST] A sphere of radius R is centered at the origin. A sketch of the sphere is shwn in the diagram. If the sphere S: x^2+y^2+z^2=R^2 is inscribed in a cylinder with radius r and height h, find the values of r and h that minimize the volume of the cylinder such that the sphere remains inscribed in the cylinder. Since the sphere is tangent to the bases and sides of the cylinder, the diameter of the sphere is the same as the diameter of the base of the cylinder, and it is equal to the height of the cylinder, so that r = R and h = 2R. For minimization of the volume, state the final values of r and h.[/INST]