document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=604250>Question 604250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular box without lid is to be made from a square cardboard area of 300 cm squared by cutting equal squares from each corner and then folding up the sides What is the maximum volume? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381096 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=381096\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular box without lid is to be made from a square cardboard area of 300 cm squared by cutting equal squares from each corner and then folding up the sides What is the maximum volume?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A side of a square piece of cardboard: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28300%29 ALIGN=MIDDLE  ALT=\"sqrt%28300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 17.32 cm, also means the base of the box will be square<BR>\n" );
document.write( "let x = length of the side of the squares removed from the 4 corners<BR>\n" );
document.write( "Dimension of the box; (17.32 - 2x) by (17.32 - 2x) by x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Vol = (17.32 - 2x)*(17.32 - 2x)*x<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300+-+69.28x+%2B+4x%5E2 ALIGN=MIDDLE  ALT=\"300+-+69.28x+%2B+4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * x<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+-+69.28x%5E2+%2B+300x ALIGN=MIDDLE  ALT=\"4x%5E3+-+69.28x%5E2+%2B+300x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is the equation<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graph this to find max volume<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+10%2C+-100%2C+500%2C+4x%5E3+-+69.28x%5E2+%2B+300x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+10%2C+-100%2C+500%2C+4x%5E3+-+69.28x%5E2+%2B+300x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "max volume occurs when x = 2.9 and is very close to 385 cu/cm </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );