document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193216>Question 1193216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Water is being poured at the rate of 15cm3/sec into an inverted cone with a diameter of 3m and a height of 6m. At what rate is the surface rising just as the tank is filled? </SPAN>\n" );
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document.write( "The volume of the cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28pi%29%28r%5E2%29h ALIGN=MIDDLE  ALT=\"%281%2F3%29%28pi%29%28r%5E2%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We are given dV/dt; we need to determine dh/dt.  So we need to express the volume as a function of h only.<br><BR>\n" );
document.write( "The full cone has height 6 and diameter 3, so its radius is 1.5.  Since the sides of the cone are straight, the radius is always 1/4 of the height.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=h%2F4 ALIGN=MIDDLE  ALT=\"r=h%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29%28pi%29%28r%5E2%29h=%281%2F3%29%28pi%29%28h%5E2%2F16%29h=%281%2F48%29%28pi%29h%5E3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15=dV%2Fdt=%28dV%2Fdh%29%28dh%2Fdt%29=%28%281%2F16%29%28pi%29h%5E2%29%28dh%2Fdt%29 ALIGN=MIDDLE  ALT=\"15=dV%2Fdt=%28dV%2Fdh%29%28dh%2Fdt%29=%28%281%2F16%29%28pi%29h%5E2%29%28dh%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2Fdt=240%2F%28%28pi%29h%5E2%29 ALIGN=MIDDLE  ALT=\"dh%2Fdt=240%2F%28%28pi%29h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "At the moment the cone is filled, the height h is 6, and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2Fdt=240%2F%2836pi%29=20%2F%283pi%29 ALIGN=MIDDLE  ALT=\"dh%2Fdt=240%2F%2836pi%29=20%2F%283pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: Just as the tank is filled, the water is rising at a rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%283pi%29 ALIGN=MIDDLE  ALT=\"20%2F%283pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm/sec<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );