document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=938257>Question 938257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the areas of two similar tetrahedrons are 24 square inches and 96 square inches. find the ratio of their volumes<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573128 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=573128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This method works only for regular tetrahedra.  Not enough info is given to calculate for irregular tetrahedra.\r<BR>\n" );
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document.write( "The formula for surface area of a regular tetrahedron is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=sqrt%283%29a%5E2 ALIGN=MIDDLE  ALT=\"SA=sqrt%283%29a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this case we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=sqrt%283%29a%5E2 ALIGN=MIDDLE  ALT=\"24=sqrt%283%29a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > solving for a:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=24%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"a%5E2=24%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=a=sqrt%2824%2Fsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"a=sqrt%2824%2Fsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=3.72 (approx.)<BR>\n" );
document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=96%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"a%5E2=96%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=a=sqrt%2896%2Fsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"a=sqrt%2896%2Fsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "a=7.44 (approx.)\r<BR>\n" );
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document.write( "The volume for a regular tetrahedron is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2F%286%28Sqrt%282%29%29%29 ALIGN=MIDDLE  ALT=\"a%5E3%2F%286%28Sqrt%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "V(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283.72%5E3%29%2F%286sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%283.72%5E3%29%2F%286sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.07 <BR>\n" );
document.write( "V(2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287.44%5E3%29%2F%286sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%287.44%5E3%29%2F%286sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 48.53\r<BR>\n" );
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document.write( "The ratio of volumes =V(1)/V(2) =6.07/48.53= 0.125 = 1:8<BR>\n" );
document.write( "Note the ratio of edge length=1:2 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    the ratio of surface area=1:4 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         the ratio of volumes=1:8 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E3 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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