document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146721>Question 1146721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good day!<BR>\n" );
document.write( "Please help me with my problem solving.<BR>\n" );
document.write( "=> Water is flowing into a conical reservoir 20 ft deep and 10 ft deep across the top at the rate of 15 ft³ per minute. Find how fast the surface is rising when the water is 8 ft deep. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #768004 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=768004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) Formula for the volume of a cone: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29 ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Use the given dimensions of the cone to get the volume formula in terms of a single variable.  Since the problem asks for the rate of change of the depth (height), we want a volume formula in terms of h.<br><BR>\n" );
document.write( "The cone has a depth of 20 and a diameter of 10, so a radius of 5.  So at all times as the cone is filling, the radius is 1/4 of the depth: r = h/4.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29%28pi%29%28%28h%2F4%29%5E2%29%28h%29+=+%281%2F48%29%28pi%29%28h%5E3%29 ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29%28pi%29%28%28h%2F4%29%5E2%29%28h%29+=+%281%2F48%29%28pi%29%28h%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) Find the derivative with respect to time:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt+=+%281%2F48%29%28pi%29%283h%5E2%2A%28dh%2Fdt%29%29+=+%281%2F16%29%28pi%29%28h%5E2%29%28dh%2Fdt%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "dV/dt is given; solve for dh/dt when h=8:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+=+%281%2F16%29%28pi%29%288%5E2%29%28dh%2Fdt%29 ALIGN=MIDDLE  ALT=\"15+=+%281%2F16%29%28pi%29%288%5E2%29%28dh%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+=+4pi%2A%28dh%2Fdt%29 ALIGN=MIDDLE  ALT=\"15+=+4pi%2A%28dh%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2Fdt+=+15%2F%284pi%29 ALIGN=MIDDLE  ALT=\"dh%2Fdt+=+15%2F%284pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: the depth of the water in the tank is changing at a rate of 15/(4pi) feet per minute when the depth is 8 feet. </SPAN>\n" );
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