document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121564>Question 1121564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> maximize the volume of a rectangular prism with surface 100. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737510 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the rectangular prism has three sides a, b, c<BR>\n" );
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document.write( "surface area(SA) = 2ab +2bc +2ac = 100<BR>\n" );
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document.write( "volume(V) = abc<BR>\n" );
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document.write( "the rectangular prism of maximum volume is a cube, therefore<BR>\n" );
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document.write( "a = b = c<BR>\n" );
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document.write( "2a^2 +2a^2 +2a^2 = 100<BR>\n" );
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document.write( "6a^2 = 100<BR>\n" );
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document.write( "a^2 = 100/6 = 50/3<BR>\n" );
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document.write( "a = 5sqrt(2/3)<BR>\n" );
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document.write( "V = a^3 = 125 * (2/3) * sqrt(2/3) = 250/3 * sqrt(2/3) approximately 68.0414 square units<BR>\n" );
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