Question

Show that the height of a closed right circular cylinder of given surface and maximum volume, is equal to the diameter of its base.

Answer 1

Let r and h be radius and height of given cylinder of surface area S.

If V be the volume of cylinder then

For maximum or minimum value of V,

Hence, for r = \(\sqrt\frac{S}{6\pi},\) Volume V is maximum.

Therefore, for maximum volume, height of cylinder is equal to diameter of its base.