document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156175>Question 1156175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help, me with this calculus homework about related rates\r<BR>\n" );
document.write( "\n" );
document.write( "Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (Round your answer to two decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778867 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=778867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) What are we supposed to find?  rate of change of height: dh/dt<br><BR>\n" );
document.write( "(2) What are we given?  rate of change of volume: dV/dt<br><BR>\n" );
document.write( "So to solve the problem, we need to get the relationship between volume V and height h.<br><BR>\n" );
document.write( "<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( "That gives us the volume in terms of r and h; so we need to get r in terms of h.<br><BR>\n" );
document.write( "The problem tells us d=h.  d = 2r; so r = (1/2)d = (1/2)h.<br><BR>\n" );
document.write( "Substitute in the volume formula:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29%28pi%29%28%281%2F2%29h%29%5E2%28h%29+=+%281%2F12%29%28pi%29%28h%5E3%29 ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29%28pi%29%28%281%2F2%29h%29%5E2%28h%29+=+%281%2F12%29%28pi%29%28h%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now you are ready to take the derivative and solve the problem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dV%2Fdt+=+%28%281%2F12%29%28pi%29%283h%5E2%29%29%28dh%2Fdt%29 ALIGN=MIDDLE  ALT=\"dV%2Fdt+=+%28%281%2F12%29%28pi%29%283h%5E2%29%29%28dh%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Plug in h=10 and the given value of dV/dt to solve for dh/dt....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );