Let R be the radius and h be the height of the cylinder which is inscribed in a sphere of radius r cm.
Then from the figure,
Let V be the volume of the cylinder.
Then V = πR2h
\(\therefore\) volume of the largest cylinder
Hence, the volume of the largest cylinder inscribed in a sphere of radius ‘r’ cm = \(\frac{4R^3}{3\sqrt{3}}\) cu cm.