document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=994582>Question 994582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Water is poured into a conical paper cup at the rate of 3/2 in^3/sec . If the cup is 6 inches tall and the top<BR>\n" );
document.write( "has a radius of 3 inches, how fast is the water level rising when the <BR>\n" );
document.write( "water is 3 inches deep?\r<BR>\n" );
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document.write( "The water level is rising at a rate of____\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 #613644 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=613644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of a cone of 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 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;\" > is given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29%2Api%2AR%5E2%2Ah ALIGN=MIDDLE  ALT=\"V=%281%2F3%29%2Api%2AR%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I am not going to keep mentioning units,<BR>\n" );
document.write( "but time, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is understood to be measured in seconds;<BR>\n" );
document.write( "<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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > are understood to be measured in inches,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > is understood to be in cubic inches.<BR>\n" );
document.write( "The cup is filling at a rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt=3%2F2 ALIGN=MIDDLE  ALT=\"dV%2Fdt=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > . <BR>\n" );
document.write( "As the water is filling the conical paper cup,<BR>\n" );
document.write( "the water is in the shape of a similar cone,<BR>\n" );
document.write( "with a radius to height ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F6=1%2F2 ALIGN=MIDDLE  ALT=\"3%2F6=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=h%2F2 ALIGN=MIDDLE  ALT=\"R=h%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The volume of water in the cup as a function of the water-cone height is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28h%29=%281%2F3%29%2Api%2A%28h%2F2%29%5E2%2Ah=%281%2F3%29%2Api%2A%28h%5E2%2F4%29%2Ah=%28pi%2F12%29%2Ah%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The inverse function is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28V%29=%2812V%2Fpi%29%5E%28%221%2F3%22%29=%2812%2Fpi%29%5E%28%221%2F3%22%29%2AV%5E%28%221%2F3%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2FdV=%2812%2Fpi%29%5E%28%221%2F3%22%29%2A%281%2F3%29%2AV%5E%28%22-2%2F3%22%29=%2812%2Fpi%29%5E%28%221%2F3%22%29%2A%281%2F27%29%5E%28%221%2F3%22%29%2AV%5E%28%22-2%2F3%22%29=%284%2F9pi%29%5E%28%221%2F3%22%29%2AV%5E%28%22-2%2F3%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%28pi%2F12%29%2A3%5E3=%28pi%2F12%29%2A9=9pi%2F4 ALIGN=MIDDLE  ALT=\"V=%28pi%2F12%29%2A3%5E3=%28pi%2F12%29%2A9=9pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2FdV=%284%2F9pi%29%5E%28%221%2F3%22%29%2A%289pi%2F4%29%5E%28%22-2%2F3%22%29=%284%2F9pi%29%5E%28%221%2F3%22%29%2A%284%2F9pi%29%5E%28%222%2F3%22%29=4%2F9pi ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2Fdt=%28dh%2FdV%29%2A%28dV%2Fdt%29=%284%2F9pi%29%2A%283%2F2%29=highlight%282%2F3pi%29 ALIGN=MIDDLE  ALT=\"dh%2Fdt=%28dh%2FdV%29%2A%28dV%2Fdt%29=%284%2F9pi%29%2A%283%2F2%29=highlight%282%2F3pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );