Q28 of 45 Page 1

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

Given; Let S be the surface area, r be the radius, h be the height, and V be the volume of the closed right circular cylinder.

⇒ S = 2πr2 + 2πrh



⇒ V = πr2h




Differentiating w.r.t x.



For maxima or minima



∴ S = 6πr2



∴ h = 2r



∴ V is maximum when h = 2r


i.e When height of a closed right circular cylinder is equal to the diameter of its base.


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