<PRE><B>Question 118107</B>
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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