document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=399060>Question 399060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular prism has a surface area of 256 sq in. What is the maximum volume it can hold?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282692 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=282692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the dimensions of the prism are L, W, H. Then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28LW+%2B+WH+%2B+LH%29+=+256 ALIGN=MIDDLE  ALT=\"2%28LW+%2B+WH+%2B+LH%29+=+256\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW+%2B+WH+%2B+LH+=+128 ALIGN=MIDDLE  ALT=\"LW+%2B+WH+%2B+LH+=+128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By the AM-GM inequality (arithmetic mean - geometric mean inequality),\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28LW+%2B+WH+%2B+LH%29%2F3+%3E=+root%283%2C+L%5E2W%5E2H%5E2%29 ALIGN=MIDDLE  ALT=\"%28LW+%2B+WH+%2B+LH%29%2F3+%3E=+root%283%2C+L%5E2W%5E2H%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128%2F3+%3E=+root%283%2C+L%5E2W%5E2H%5E2%29 ALIGN=MIDDLE  ALT=\"128%2F3+%3E=+root%283%2C+L%5E2W%5E2H%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cubing both sides,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128%5E3%2F3%5E3+%3E=+L%5E2W%5E2H%5E2 ALIGN=MIDDLE  ALT=\"128%5E3%2F3%5E3+%3E=+L%5E2W%5E2H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128%5E3%2F3%5E3%29+%3E=+LWH ALIGN=MIDDLE  ALT=\"sqrt%28128%5E3%2F3%5E3%29+%3E=+LWH\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this value is the maximum volume of the prism, which occurs when the solid is a cube. </SPAN>\n" );
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