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Question 118107: hi please help me with this question. i dont know what to do
The inside of an aircraft is a square based prism and will be built usin 4 m (squared) of of aluminum. Th plane or cockpit needs a floor, ceiling and three walls. What demensions will maximize the volume of the cockpit. Round out the deminsions to the nearest meter.
thanks for any help coming this way
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The inside of an aircraft is a square based prism and will be built usin 4 m (squared) of of aluminum.
The plane or cockpit needs a floor, ceiling and three walls.
What dimensions will maximize the volume of the cockpit.
Round out the dimensions to the nearest meter.
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Volume = Bh where base and ceiling are both squares.
Then the total side area is 4-2x^2 sq meters
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Assuming all sides are of equal area,
Each side has area = (1/3)(4-2x^2)
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The base of each side is x so the height is(1/3x)(4-2x^2)/3x=(2/3x)(2-x^2)
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Then the Volume of the cockpit = Bh = x^2[(2/3x)(2-x^2)]
= (2x/3)(2-x^2) cu. meters
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Graphing this and looking for the maximum volume I find:
Volume= 0.7258 cu meters when x = 0.8165
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Cheers,
Stan H.
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