Answer :
Let r and h be the radius and the height of the cylinder respectively.
Now, h =
The volume (V) of the cylinder is given by:
V = πr2h =2 πr2
Now, if
Now,
Now, we can see that at, ,
< 0.
Therefore, the volume is the maximum when.
When , the height of the cylinder is
.
Therefore, the volume of the cylinder is the maximum when the height of the cylinder is .
Hence Proved.
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