Answer :

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

Then, the surface area (S) of the cylinder is given by:


S = 2πr2 + 2πrh


h



Let V be the volume of the cylinder. Then


V = πr2h



Now,


If


So, when then <0


Then, by second derivative test, the volume is the maximum when


Now, when . then h =


Therefore, the volume is the maximum when the height is the twice the radius or height is equal to diameter.


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