document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939782>Question 939782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonal of one cube has a length of 22cm. A diagonal of another cube is 42cm. The larger cube has a volume of 64cm^3. Find the volume of the smaller cube. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572722 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3Cy ALIGN=MIDDLE  ALT=\"x%3Cy\"   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=system%28x%5E2%2Bx%5E2%2Bx%5E2=d%5E2%2Cy%5E2%2By%5E2%2By%5E2=D%5E2%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2%2Bx%5E2%2Bx%5E2=d%5E2%2Cy%5E2%2By%5E2%2By%5E2=D%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=system%28d=sqrt%283x%5E2%29%2CD=sqrt%283y%5E2%29%29 ALIGN=MIDDLE  ALT=\"system%28d=sqrt%283x%5E2%29%2CD=sqrt%283y%5E2%29%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=system%28x%2Asqrt%283%29=d%2Cy%2Asqrt%283%29=D%29 ALIGN=MIDDLE  ALT=\"system%28x%2Asqrt%283%29=d%2Cy%2Asqrt%283%29=D%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=x=d%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"x=d%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=D%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"y=D%2Fsqrt%283%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=y%2Fx=D%2Fd ALIGN=MIDDLE  ALT=\"y%2Fx=D%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Look specifically at the larger cube seemingly diagonal 42 and volume 64.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=D%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"y=D%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=42%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"y=42%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rationalize denom;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"42sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=14%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"y=14%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the proportion earlier found.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=yD%2Fd ALIGN=MIDDLE  ALT=\"x=yD%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14%2Asqrt%283%29%2A64%2F22 ALIGN=MIDDLE  ALT=\"x=14%2Asqrt%283%29%2A64%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x=7%2A64%2Asqrt%283%29%2F11%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=7%2A64%2Asqrt%283%29%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----side length of the smaller cube, so raise all this to power 3 to get volume.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%5E3=122.18181818%2Asqrt%283%29=highlight%28%28122%262%2F11%29sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"v=x%5E3=122.18181818%2Asqrt%283%29=highlight%28%28122%262%2F11%29sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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