document.write( "Question 227484: 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( " \n" ); document.write( "

Algebra.Com's Answer #169366 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
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( ":
\n" ); document.write( "If squares with a side x, are removed from each corner, the dimensions of the box:
\n" ); document.write( "(30-2x) by (18-2x) by x
\n" ); document.write( ":
\n" ); document.write( "V = H * L * W
\n" ); document.write( ":
\n" ); document.write( "V = x*(18-2x)*(30-2x)
\n" ); document.write( "FOIL
\n" ); document.write( "V = x(540 - 36x - 60x + 4x^2)
\n" ); document.write( ":
\n" ); document.write( "V = x(4x^2 - 96x + 540)
\n" ); document.write( ":
\n" ); document.write( "V(x) = 4x^3 - 96x^2 + 540x \n" ); document.write( "

\n" );