document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=611580>Question 611580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two vertices of a cube have coordinates A(5, 12, 12) and B(20, 28, 24). What is the smallest possible volume of the cube? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385049 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=385049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two vertices of a cube have coordinates A(5,12,12) and B(20,28,24). What is the smallest possible volume of the cube?<BR>\n" );
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document.write( "A and B can be on the same edge, diagonally on the same face, or diagonally thru the center of the cube.<BR>\n" );
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document.write( "The distance AB is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28diffx%5E2+%2B+diffy%5E2+%2B+diffz%5E2%29+=+sqrt%2815%5E2+%2B+16%5E2+%2B+12%5E2%29+=+sqrt%28625%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "AB = 25<BR>\n" );
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document.write( "If AB is an edge, volume = 25^3 = 15625<BR>\n" );
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document.write( "If AB is a diagonal on a face, the edges are 5sqrt(2)/2 --> Vol =~ 44.19<BR>\n" );
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document.write( "If AB is a diagonal thru the center, the edges are 5sqrt(3)/3 --> Vol =~ 24.056<BR>\n" );
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