17) Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is
. Also, find the maximum volume.
The volume of the cylinder (V) =
By Pythagoras theorem in
h = 2OA
Now,
Hence, the point is the point of maxima
Hence, the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is
and maximum volume is