document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309443>Question 309443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of an open box with a square base and rectangular sides us 250 cubed inches. if sides are double thickness and the bottom is triple thickness, what size box will use the least amount of material? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221371 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=221371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of an open box with a square base and rectangular sides us 250 cubed inches.<BR>\n" );
document.write( " if sides are double thickness and the bottom is triple thickness, what size box will use the least amount of material?<BR>\n" );
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document.write( "Surface area of an open box with a square base<BR>\n" );
document.write( "x = side of the square base<BR>\n" );
document.write( "h = height of the box<BR>\n" );
document.write( "S.A = x^2 + 4(x*h)<BR>\n" );
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document.write( "Surface area required with a triple thickness bottom and double thickness sides<BR>\n" );
document.write( "S.A. = 3x^2 + 8(x*h)<BR>\n" );
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document.write( "Vol = x^2*h<BR>\n" );
document.write( "x^2*h = 250<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2Fx%5E2 ALIGN=MIDDLE  ALT=\"250%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "S.A = 3x^2 + 8(x*h)<BR>\n" );
document.write( "Substitute for h<BR>\n" );
document.write( "S.A. = 3x^2 + 8(x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2Fx%5E2 ALIGN=MIDDLE  ALT=\"250%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "S.A. = 3x^2 + 8(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2Fx ALIGN=MIDDLE  ALT=\"250%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "S.A. = 3x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000%2Fx ALIGN=MIDDLE  ALT=\"2000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plot this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+16%2C+-200%2C+1000%2C+3x%5E2+%2B+%282000%2Fx%29+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+16%2C+-200%2C+1000%2C+3x%5E2+%2B+%282000%2Fx%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "You can see min material for surface area occurs when x = 7<BR>\n" );
document.write( "Find the height<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2F7%5E2 ALIGN=MIDDLE  ALT=\"250%2F7%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 5.1 inches<BR>\n" );
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document.write( "Least amt of material used in a 7 by 7 by 5.1 inch box<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );