document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172105>Question 1172105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A closed box, whose length is thrice its width, is to have a surface of 200 square cm. Find the maximum Volume 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 #797012 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "Total Surface Area = 6x^2 (top and bottom) + 8xh (4 sides) = 200 cm^2<BR>\n" );
document.write( "Tot SA = 6x^2 + 8xh = 200<BR>\n" );
document.write( "Finding 'x' value of 'h'<BR>\n" );
document.write( "8xh = 200 - 6x^2<BR>\n" );
document.write( "h = (200 - 6x^2)/8x<BR>\n" );
document.write( "Cancelling 2 top and bottom<BR>\n" );
document.write( "h = (100 - 3x^2)/4x\r<BR>\n" );
document.write( "\n" );
document.write( "Volume = length * breadth * height   (Using * for multiply)<BR>\n" );
document.write( "V= 3x * x * h<BR>\n" );
document.write( "V = 3x^2h<BR>\n" );
document.write( "Bringing in 'x' value for 'h'<BR>\n" );
document.write( "V(x) = 3x^2(100 - 3x^2)/4x<BR>\n" );
document.write( "3/4x (100 - 3x^2)<BR>\n" );
document.write( "V(x) = (300/4)x - 9x^3/4<BR>\n" );
document.write( "Cancel down<BR>\n" );
document.write( "V(x) = 75x - 9x^3/4<BR>\n" );
document.write( "Differentiate<BR>\n" );
document.write( "V'(x) = 75 - 27x^2/4<BR>\n" );
document.write( "Make V'(x) = 0<BR>\n" );
document.write( "75 - 27x^2/4 = 0<BR>\n" );
document.write( "-27x^2/4 = - 75<BR>\n" );
document.write( "Multiply both sides by -1<BR>\n" );
document.write( "27x^2/4 = 75<BR>\n" );
document.write( "27x^2 = 300<BR>\n" );
document.write( "x^2 = 300/27 or 100/9 <BR>\n" );
document.write( "x = 10/3.\r<BR>\n" );
document.write( "\n" );
document.write( ".........................................................  -    10/3    +<BR>\n" );
document.write( "Nature Table.75 - 27x^2/4 ...... +     0      -<BR>\n" );
document.write( " ........................................................... /     -      \         <BR>\n" );
document.write( "Maximum<BR>\n" );
document.write( "height = (100 - 3x^2)/4x<BR>\n" );
document.write( "Height = [100 - 3(10/3)^2]  / 4 (10/3)<BR>\n" );
document.write( "Height = 5 cm<BR>\n" );
document.write( "Total Volume = length * breadth * height<BR>\n" );
document.write( "Total volume = 3(10/3) * (10/3) * 5<BR>\n" );
document.write( "Total Volume = 10 * 10/3 * 5<BR>\n" );
document.write( "Total volume = 166.66 cm^3   <BR>\n" );
document.write( "Hope this helps :-)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );