SOLUTION: The corners of a piece of paper are cut to make an open top box. The cut corners are 0.5 in by 0.5 in. If the width of the paper is two-thirds the height what, what are the dime

Question 1075200: The corners of a piece of paper are cut to make an open top box. The cut corners are 0.5 in by 0.5 in. If the width of the paper is two-thirds the height what, what are the dimensions of the paper if the volume is to be 60 cubic inches?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The corners of a piece of paper are cut to make an open top box. The cut corners are 0.5 in by 0.5 in. If the width of the paper is two-thirds the height what, what are the dimensions of the paper if the volume is to be 60 cubic inches?
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width = (2/3)h inches
height = h inches
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After cutting the corners::
width = (2/3)h - 1 inches
height = h - 1 inches
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Volume Equation:
h(h-1)((2/3)h-1) = 60 cu in
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h((2/3)h^2 - (5/3)h + 1) = 60
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(2/3)h^3 - (5/3)h^2 + h - 60 = 0
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Take the derivative::
V'(h) = 2h^2 - (10/3)h + 1
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Solve V'(h) = 0
h = 1.274 inches (height of the paper)
(2/3)h = 0.523 inches (width of the paper)
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Cheers,
Stan H.
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