SOLUTION: from a thin piece of cardboard 40in. by 40in., square corners are cut out so that the sides can be foled to make a box. what dimensions will yield a bos of maximum volume? what is

Algebra ->  Volume -> SOLUTION: from a thin piece of cardboard 40in. by 40in., square corners are cut out so that the sides can be foled to make a box. what dimensions will yield a bos of maximum volume? what is       Log On


   

Question 293406: from a thin piece of cardboard 40in. by 40in., square corners are cut out so that the sides can be foled to make a box. what dimensions will yield a bos of maximum volume? what is the maximum volume?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
from a thin piece of cardboard 40in. by 40in., square corners are cut out so that the sides can be folded to make a box.
what dimensions will yield a box of maximum volume?
what is the maximum volume?
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Volume = height*length*width
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V = x(40-2x)(40-2x)
V = 4x(20-x)(20-x)
V = 4x[400-40x+x^2)
V = 4x^3 - 160x^2 + 1600x
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Take the derivative:
V' = 12x^2 - 320x + 1600
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Solve 4(3x^2-80x+400) = 0
4(3x-20)(x-20) = 0
Realistic value for "x":
3x = 20
x = 20/3 = 6 2/3
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Volume when x = 20/3 inches
V(20/3) = 4740.7 cu. inches
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Cheers,
Stan H.
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