document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181234>Question 1181234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://media.discordapp.net/attachments/723023718497910816/849263694005403738/unknown.png?width=364&height=117 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811155 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811155\">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=+V+=+pi%2Ar%5E2%2Ah%2F3+ ALIGN=MIDDLE  ALT=\"+V+=+pi%2Ar%5E2%2Ah%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You are given r=6cm, h=20cm<br>\r<BR>\n" );
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document.write( "The answer can now be determined immediately.  How does the volume depend on h?  [ That is, is it nonlinear, linear, or not dependent at all ? ]<br>\r<BR>\n" );
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document.write( "The LONG way also works:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D+=+pi%286%29%5E2%2820%29%2F3+ ALIGN=MIDDLE  ALT=\"V%5Bo%5D+=+pi%286%29%5E2%2820%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D+ ALIGN=MIDDLE  ALT=\"V%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Volume of 2nd cone with same radius, and half the volume<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D+ ALIGN=MIDDLE  ALT=\"V%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29V%5Bo%5D ALIGN=MIDDLE  ALT=\"%281%2F2%29V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29pi%2A6%5E2%2A20%2F3+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29pi%2A6%5E2%2A20%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "But, also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2A6%5E2%2Ah%5B1%5D%2F3+ ALIGN=MIDDLE  ALT=\"+pi%2A6%5E2%2Ah%5B1%5D%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B1%5D ALIGN=MIDDLE  ALT=\"h%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the new height\r<BR>\n" );
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document.write( "Set these last two (Right hand sides) equal <br>\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29pi%2A6%5E2%2A20%2F3+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29pi%2A6%5E2%2A20%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++pi%2A6%5E2%2Ah%5B1%5D%2F3+ ALIGN=MIDDLE  ALT=\"++pi%2A6%5E2%2Ah%5B1%5D%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <br>\r<BR>\n" );
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document.write( "Note the cancellations:<BR>\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29cross%28pi%29%2Across%286%5E2%29%2A20%2Fcross%283%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29cross%28pi%29%2Across%286%5E2%29%2A20%2Fcross%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++cross%28pi%29%2Across%286%5E2%29%2Ah%5B1%5D%2Fcross%283%29+ ALIGN=MIDDLE  ALT=\"++cross%28pi%29%2Across%286%5E2%29%2Ah%5B1%5D%2Fcross%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <br>\r<BR>\n" );
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document.write( "...leaving:<BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281%29+ ALIGN=MIDDLE  ALT=\"+h%281%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2A20+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2A20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10cm ALIGN=MIDDLE  ALT=\"+10cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Understanding the linear relationship between V and h saves a lot of time.\r<BR>\n" );
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document.write( "EDIT 6/2:<BR>\n" );
document.write( "Sorry, yes, I had the cone flipped upside down so the base was at the bottom.<BR>\n" );
document.write( "Of course, I should have realized that makes no sense from a water-filling standpoint! <BR>\n" );
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