document.write( "Question 253460: An open top box with a square base is to be constructed from a sheet metal in such a way that the completed box is made of 2m^2 of the sheet metal. Express the volume of the box as a function of the width of the base. \n" ); document.write( "
Algebra.Com's Answer #186041 by ankor@dixie-net.com(22740)\"\" \"About 
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An open top box with a square base is to be constructed from a sheet metal in such a way that the completed box is made of 2m^2 of the sheet metal.
\n" ); document.write( " Express the volume of the box as a function of the width of the base.
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\n" ); document.write( "The side of a square piece of sheet metal of 2 sq/m = \"sqrt%282%29\" m
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\n" ); document.write( "Let x = side of the square base of the box
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\n" ); document.write( "let h = side of the 4 small squares removed from the square sheet to make the box
\n" ); document.write( "Also h = the height of the open box
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\n" ); document.write( "x = \"sqrt%282%29+-+2h\"
\n" ); document.write( "solve in terms of h
\n" ); document.write( "2h = \"sqrt%282%29+-+x\"
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\n" ); document.write( "h = \"%28sqrt%282%29+-+x%29%2F2\"
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\n" ); document.write( "Vol = x^2 * h
\n" ); document.write( "replace h with \"%28sqrt%282%29+-+x%29%2F2\"
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\n" ); document.write( "V(x) = \"x%5E2+%2A+%28%28sqrt%282%29+-+x%29%2F2%29\"
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\n" ); document.write( "Max vol occurs when x = .9 m, find h
\n" ); document.write( "h = \"%28sqrt%282%29+-+.9%29%2F2\"
\n" ); document.write( "h = .26 m
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\n" ); document.write( ".9^2 * .26 = .21 cu meters
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