The volume of a cylinder is (pi)r^2h and the volume of a sphere is 4/3(pi)r^3, where r is the radius of each and h is the height of the cylinder. If the sphere and cylinder have the same diameter they must have the same radius. If h=36 we can write: (pi)r^2*36=4/3(pi)r^3. Dividing both sides by (pi)r^2 we get 36=4r/3, so r=3/4*36=27. Their common radius is 27cm.