Question

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is2R/√3 . Also find the maximum volume.

Answer 1

A sphere of fixed radius (R) is given.
Let r and h be the radius and the height of the cylinder respectively.

From the given figure, we have 
The volume (V) of the cylinder is given by,

Hence, the volume of the cylinder is the maximum when the height of the cylinder is 2R/√3