document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912071>Question 912071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylinder is inscribed in a cone with height 10 and a base of radius 5, as shown below on the link. Find the approximate values of r and h for which the volume of the cylinder is a maximum. Then give the approximate maximum volume.  \r<BR>\n" );
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document.write( "http://postimg.org/image/tewn41qu7/\r<BR>\n" );
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document.write( "Thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553770 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is a relationship between <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=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5 ALIGN=MIDDLE  ALT=\"r=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0 ALIGN=MIDDLE  ALT=\"r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=10 ALIGN=MIDDLE  ALT=\"h=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So then using the point-slope form of a line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-10=%28%2810-0%29%2F%280-5%29%29%28r-0%29 ALIGN=MIDDLE  ALT=\"h-10=%28%2810-0%29%2F%280-5%29%29%28r-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-10=-2r ALIGN=MIDDLE  ALT=\"h-10=-2r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=10-2r ALIGN=MIDDLE  ALT=\"h=10-2r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the volume of the cylinder is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"V=pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=pi%2Ar%5E2%2810-2r%29 ALIGN=MIDDLE  ALT=\"V=pi%2Ar%5E2%2810-2r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To maximize the volume, take the derivative of the volume and set it equal to zero (use the chain rule).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt=pi%2A%28r%5E2%28-2%29%2B%2810-2r%29%282r%29%29 ALIGN=MIDDLE  ALT=\"dV%2Fdt=pi%2A%28r%5E2%28-2%29%2B%2810-2r%29%282r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt=pi%2A%28-2r%5E2%2B%2820r-4r%5E2%29%29 ALIGN=MIDDLE  ALT=\"dV%2Fdt=pi%2A%28-2r%5E2%2B%2820r-4r%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt=pi%2A%2820r-6r%5E2%29 ALIGN=MIDDLE  ALT=\"dV%2Fdt=pi%2A%2820r-6r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt=2pi%2Ar%2810-3r%29 ALIGN=MIDDLE  ALT=\"dV%2Fdt=2pi%2Ar%2810-3r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-3r=0 ALIGN=MIDDLE  ALT=\"10-3r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3r=-10 ALIGN=MIDDLE  ALT=\"-3r=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=10%2F3 ALIGN=MIDDLE  ALT=\"r=10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=10-2%2810%2F3%29 ALIGN=MIDDLE  ALT=\"h=10-2%2810%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=10-20%2F3 ALIGN=MIDDLE  ALT=\"h=10-20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=30%2F3-20%2F3 ALIGN=MIDDLE  ALT=\"h=30%2F3-20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=10%2F3 ALIGN=MIDDLE  ALT=\"h=10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bmax%5D=pi%2A%2810%2F3%29%5E2%2A%2810%2F3%29 ALIGN=MIDDLE  ALT=\"V%5Bmax%5D=pi%2A%2810%2F3%29%5E2%2A%2810%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bmax%5D=%281000%2F27%29pi ALIGN=MIDDLE  ALT=\"V%5Bmax%5D=%281000%2F27%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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