document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224025>Question 224025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give 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 #167395 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume?\r<BR>\n" );
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document.write( "Step 1.  The maximum volume is when the rectangle is a square and let s be the side of the square.\r<BR>\n" );
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document.write( "Step 2.  The perimeter P of a rectangle (or square) means adding up all four sides.  So P=s+s+s+s=4s since all four sides of the square are equal.\r<BR>\n" );
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document.write( "Step 3.  But P=36=4s.  Solving for s=36/4=9 cm.\r<BR>\n" );
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document.write( "Step 4.  Volume V=A*h of the box where A is the area of the square and h is the height given as h=4.\r<BR>\n" );
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document.write( "Step 5.  Area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=s%5E2 ALIGN=MIDDLE  ALT=\"A=s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a square.  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=9%5E2=81 ALIGN=MIDDLE  ALT=\"A=9%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > square centimeters.\r<BR>\n" );
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document.write( "Step 6.  Then V=A*h=81*4=324 cubic centimeters.\r<BR>\n" );
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document.write( "Step 7.  ANSWER:  The maximum volume of the box is 324 cubic centimeters.\r<BR>\n" );
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document.write( "I hope the above steps and explanation were helpful. \r<BR>\n" );
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document.write( "For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for \r<BR>\n" );
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document.write( "Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry. \r<BR>\n" );
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document.write( "Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.\r<BR>\n" );
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document.write( "Respectfully, <BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV\r<BR>\n" );
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document.write( " </SPAN>\n" );
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