document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102126>Question 1102126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a conical tank with vertex at the bottom is being filled at a rate of 4 cubic m per minute. the tank is 24 m deep and 12 m at the top. find the rate of change of the depth of the waste when the water id 8m deep </SPAN>\n" );
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document.write( "You didn't specify whether the 12m is the radius or the diameter of the top of the tank.  By the way you state the problem, I assume it is the full width (diameter) of the top of the tank.<br><BR>\n" );
document.write( "Then the radius of the top of the tank is 6m; since the depth of the tank is 24m, the radius is 1/4 of the depth.  As the tank is being filled, the volume of water forms a cone that is similar to the whole tank; so at any time the radius of the surface of the water in the tank is 1/4 the depth of the water.<br><BR>\n" );
document.write( "So the volume of water when the depth is h is<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%28%28h%2F4%29%5E2%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=dV%2Fdt+=+%281%2F16%29%28pi%29h%5E2%28dh%2Fdt%29 ALIGN=MIDDLE  ALT=\"dV%2Fdt+=+%281%2F16%29%28pi%29h%5E2%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+=+%2816%2F%28%28pi%29h%5E2%29%29%2A%28dV%2Fdt%29 ALIGN=MIDDLE  ALT=\"dh%2Fdt+=+%2816%2F%28%28pi%29h%5E2%29%29%2A%28dV%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We know dV/dt is 4; when the depth h is 4, dh/dt is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2816%2F%28%28pi%294%5E2%29%29%2A4%29+=+4%2Fpi ALIGN=MIDDLE  ALT=\"%28%2816%2F%28%28pi%294%5E2%29%29%2A4%29+=+4%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );