document.write( "Question 52767: An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
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Algebra.Com's Answer #35196 by ankor@dixie-net.com(22740)\"\" \"About 
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An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
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\n" ); document.write( "a) Find the function V that represents the volume of the box in terms of x.
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\n" ); document.write( "The bottom dimensions: [8-2x] by [6-2x]; the height would be just 'x'
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\n" ); document.write( "Vol = Length * Width * Height
\n" ); document.write( "Vol = [8-2x] * [6-2x] * x
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\n" ); document.write( "FOIL Length * Width
\n" ); document.write( "Vol = [48 - 28x + 4x^2] * x
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\n" ); document.write( "Mult that by x (height) and you have
\n" ); document.write( "Vol = 48x - 28x^2 + 4x^3
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\n" ); document.write( "V(x) = 4x^3 - 28x^2 + 48x\r
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\n" ); document.write( "\n" ); document.write( "An example: a box 1 ft high: [8-2] * [6-2] * 1 = 24 cu ft.
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\n" ); document.write( "Check our equation for x=1: substitute 1 for x in the equation and you have: 4 - 28 + 48 = +24.\r
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