document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407197>Question 407197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a cylinder of height h cm and radius r cm stands on a table. a cone of height H cm is placed over the cylinder and the rests on the table wit the top of the cylinder touching the inside of the cone. the ratio r:R is 2:5<BR>\n" );
document.write( "use the given ratio to write an expression for r in terms of R </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287069 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287069\">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=r%2FR+=+2%2F5 ALIGN=MIDDLE  ALT=\"r%2FR+=+2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%282%2F5%29R ALIGN=MIDDLE  ALT=\"r+=+%282%2F5%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On a related note, you can actually find a relationship between h and H:\r<BR>\n" );
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document.write( "A vertical cross-section passing through the apex of the cone produces two similar right triangles:<BR>\n" );
document.write( "The top triangle has horizontal leg r and vertical leg H - h.<BR>\n" );
document.write( "The bottom triangle has horizontal leg R - r and vertical leg h.  Hence<BR>\n" );
document.write( "by similarity of triangles,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F%28R+-+r%29+=+%28H+-+h%29%2Fr ALIGN=MIDDLE  ALT=\"h%2F%28R+-+r%29+=+%28H+-+h%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hr+=+%28H+-+h%29%28R+-+r%29 ALIGN=MIDDLE  ALT=\"hr+=+%28H+-+h%29%28R+-+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hr+=+HR+-+Hr+-+hR++%2Bhr ALIGN=MIDDLE  ALT=\"hr+=+HR+-+Hr+-+hR++%2Bhr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Hr+=+%28H+-+h%29R ALIGN=MIDDLE  ALT=\"Hr+=+%28H+-+h%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28%28H+-+h%29%2FH%29R ALIGN=MIDDLE  ALT=\"r+=+%28%28H+-+h%29%2FH%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%282%2F5%29R ALIGN=MIDDLE  ALT=\"r+=+%282%2F5%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find a relationship between h and H. </SPAN>\n" );
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