The volume of the cylinder from the rectangle is the size of the cylinder
The rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
<h3>How to determine the rectangle</h3>
Let the dimension of the rectangle be x and y.
So, the perimeter (P) is:
The perimeter is given as 18.
So, we have:
Divide both sides by 2
Make y the subject
The volume of a cylinder is:
So, we have:
Expand
Differentiate
Set to 0
Divide both sides by
Divide both sides by 3x
Make x the subject
Recall that:
So, we have:
Hence, the rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
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