document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962250>Question 962250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open rectangular box with square base and open top is to contain 1000cm^3.Find the dimensions that require the least amount of material.Neglect the thickness of the material and waste in construction.(Hint:Here we are looking at surface area)\r<BR>\n" );
document.write( "\n" );
document.write( "Help me.<BR>\n" );
document.write( "Style. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587969 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=587969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An open rectangular box with square base and open top is to contain 1000cm^3.<BR>\n" );
document.write( "Find the dimensions that require the least amount of material.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let x = side of the square base<BR>\n" );
document.write( "let h = the height of the box<BR>\n" );
document.write( "then the volume<BR>\n" );
document.write( "x * x * h = 1000<BR>\n" );
document.write( "x^2h = 1000<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2Fx%5E2 ALIGN=MIDDLE  ALT=\"1000%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The surface area of an open box<BR>\n" );
document.write( ":<BR>\n" );
document.write( "S.A. = bottom area + 4 side areas<BR>\n" );
document.write( "S.A. = x^2 + 4(x*h)<BR>\n" );
document.write( "Replace h with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2Fx%5E2 ALIGN=MIDDLE  ALT=\"1000%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >}<BR>\n" );
document.write( "S.A. = x^2 + 4(x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2Fx%5E2 ALIGN=MIDDLE  ALT=\"1000%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "cancel x into x^2<BR>\n" );
document.write( "S.A. = x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4000%2Fx ALIGN=MIDDLE  ALT=\"4000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph this in your graphing calc S.A. = y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+20%2C+-200%2C+1000%2C+x%5E2%2B%284000%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+20%2C+-200%2C+1000%2C+x%5E2%2B%284000%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "minimum surface when x = 12.6 cm the side of the square base<BR>\n" );
document.write( "Find the height<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F12.6%5E2 ALIGN=MIDDLE  ALT=\"1000%2F12.6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F158.76 ALIGN=MIDDLE  ALT=\"1000%2F158.76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 6.3 cm is the height<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Summarize, 12.6 by 12.6 by 6.3 dimensions for minimum surface area<BR>\n" );
document.write( ":<BR>\n" );
document.write( "confirm this by finding the volume with these dimension<BR>\n" );
document.write( "12.6 * 12.6 * 6.3 = 1000.2, close enough <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );