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


Let V be the volume of the cylinder.

Therefore, V = πr2h

…….Using equation 1

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


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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