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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