document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=717051>Question 717051</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two circular cylinders have the same altitude. Find the ratio of their volumes if the radius of one cylinder is 5 times the diameter of the other. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440071 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=440071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of a cylinder is calculated as the surface area of its base times the height.<BR>\n" );
document.write( " <BR>\n" );
document.write( "CORRECTED CORRECTION:<BR>\n" );
document.write( "This is what happens when you reach retirement age.<BR>\n" );
document.write( "If the radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > of one cylinder is 5 times the diameter of the other,<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=5%2A%282r%29 ALIGN=MIDDLE  ALT=\"R=5%2A%282r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=10r ALIGN=MIDDLE  ALT=\"R=10r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the ratio of volumes will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2=highlight%28100%29 ALIGN=MIDDLE  ALT=\"10%5E2=highlight%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "OOPS! It was not 2 times! My previous solution below is the answer to the problem in my head, as I (mis)remembered it, not the answer to the problem as written above.<BR>\n" );
document.write( "The two cylinders have height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and radii <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r ALIGN=MIDDLE  ALT=\"2r\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in the dictionary, the word radiuses is allowed as a plural, but spellchecker does not like it).<BR>\n" );
document.write( "Their volumes will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%282r%29%5E2%2Ah=pi%2A4r%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2A%282r%29%5E2%2Ah=pi%2A4r%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so the ratio of their volumes is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A4r%5E2%2Ah%2F%28pi%2Ar%5E2%2Ah%29=highlight%284%29 ALIGN=MIDDLE  ALT=\"pi%2A4r%5E2%2Ah%2F%28pi%2Ar%5E2%2Ah%29=highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 4:1 if you prefer to express it that way.<BR>\n" );
document.write( "The larger cylinder has a volume that is 4 times the volume of the smaller one. </SPAN>\n" );
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