document.write( "Question 342277: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. \n" ); document.write( "
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A box with an open top is to be constructed from a rectangular piece of cardboard
\n" ); document.write( " with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each
\n" ); document.write( " corner and then folding up the sides as in the figure.
\n" ); document.write( "Express the volume V of the box as a function of x.
\n" ); document.write( ":
\n" ); document.write( "Let x = side of the square
\n" ); document.write( "then the box dimensions (Length,Width,Height) will be:
\n" ); document.write( "(18-2x) by (30-2x) by x
\n" ); document.write( "Vol = (18-2x)*(30-2x)*x
\n" ); document.write( "V = (540 - 36x - 60x + 4x^2)* x
\n" ); document.write( "The volume as a function of x
\n" ); document.write( "V(x) = 4x^3 - 96x^2 + 540x \n" ); document.write( "
\n" );