Question

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R/√3. Also, find the maximum Volume.

Answer 1

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.