The height of the cylinder of maximum volume that can be inscribed in a sphere of radius ‘a’ is

Let h be the height and r be the radius of the cylinder. Let O be the centre of the sphere from diagramOA2=OP2+PA2a2=h24+r2...........1V=πr2h=πh.a2−h24V=πa2h−π4h3dvdh=πa2−π43h2d2vdh2=0−3π42h<0V is either max or mindvdh=0⇒h=2a3