Answer :

Let r be the radius of the base and h the height of a cylinder.


The surface area is given by,


S = 2 π r2 + 2 π rh


………(1)


Let V be the volume of the cylinder.


Therefore, V = πr2h


…….Using equation 1



Differentiating both sides w.r.t r, we get,


……….(2)


For maximum or minimum, we have,




S = 6πr2


2πr2 + 2πrh = 6πr2


h = 2r


Differentiating equation 2, with respect to r to check for maxima and minima, we get,



Hence, V is maximum when h = 2r or h = diameter


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