SOLUTION: Suppose that the height of a box is to be 1 foot. Determine which shape for the bottom of the box will give you the greatest volume if the perimeter of the bottom of the box must

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Question 92379: Suppose that the height of a box is to be 1 foot. Determine which shape for the bottom of the box will give you the greatest volume if the perimeter of the bottom of the box must be 3.125 feet.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Suppose that the height of a box is to be 1 foot. Determine which shape for the bottom of the box will give you the greatest volume if the perimeter of the bottom of the box must be 3.125 feet.
:
This is a special case which can be done with one simple calculation. Since the
height is 1, the value of the volume will be the same value as the area of the
base. Max area of a rectangle is a square. Therefore the bottom will be a square.
:
The max volume will be (3.125/4)^2 * 1 = .61035 cu ft