document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143541>Question 143541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same time water is being pumped into the tank at a constant rate. The tank has a height of 6m and a diameter of 10 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2m, find the rate at which the water is being pumped into the tank. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104475 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"The tank has a height of 6m and a diameter of 10 m\" __ 6/10=H/(2r) __ 12r=10H __ r=(5/6)H\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "V=(1/3)(pi)(r^2)(H) __ substituting __ V=(1/3)(pi)[(5/6)H]^2(H) __ V=(25/108)(pi)(H^3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "differentiaitng __ dV=(25/108)(pi)(3)(H^2)(dH) __ dV=(25/36)(pi)(H^2)(dH)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x=\"rate at which the water is being pumped into the tank\" __ working in cm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x-10000=(25/36)(pi)(200^2)(20) __ x=1.76X10^6cm^3/min (approx)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );