document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147149>Question 147149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A container is to be designed that is a rectangilar box with an open top that will hold 108 cubic inches.  If x= the length of the side of the base, then express the surface area of the box as a function of X.  What is domain of this function and determine the dimensions of the box that minimizes the surface area of the box </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107481 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=107481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A container is to be designed that is a rectangular box with an open top that will hold 108 cubic inches.  If x = the length of the side of the base, then express the surface area of the box as a function of X.  What is domain of this function and determine the dimensions of the box that minimizes the surface area of the box<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Assume the base is square with an area = x^2.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let h = height of the box<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The volume equation<BR>\n" );
document.write( "x^2 * h = 108<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2Fx%5E2 ALIGN=MIDDLE  ALT=\"108%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Surface area:<BR>\n" );
document.write( "Bottom = x^2<BR>\n" );
document.write( "4 sides = 4(x<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2Fx%5E2 ALIGN=MIDDLE  ALT=\"108%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2Fx ALIGN=MIDDLE  ALT=\"432%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >; area of the 4 sides<BR>\n" );
document.write( ":<BR>\n" );
document.write( "S.A. = x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2Fx ALIGN=MIDDLE  ALT=\"432%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graph: y = x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2Fx ALIGN=MIDDLE  ALT=\"432%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+20%2C+-30%2C+200%2C+x%5E2%2B%28432%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+20%2C+-30%2C+200%2C+x%5E2%2B%28432%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Min surface area: x = 6<BR>\n" );
document.write( "Find h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F6%5E2 ALIGN=MIDDLE  ALT=\"108%2F6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3 inches<BR>\n" );
document.write( ":<BR>\n" );
document.write( "min surface area of the box: 6^2 + 4(6*3) = 108 sq inches<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Interesting that the vol and surface area are equal.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Domain of the equation: x > 0 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );