document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119545>Question 1119545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the rate at which the volume of a right circular cylinder of constant altitude 10ft changes with respect to its diameter when the radius is 5ft is zero. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735424 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=735424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem makes no sense:  \"...when the radius is 5 ft is zero.\"<br><BR>\n" );
document.write( "I can only assume that the question was supposed to read \"... when the radius is 5 feet.\"<br><BR>\n" );
document.write( "The formula for the volume of a cylinder is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28r%5E2%29%28h%29 ALIGN=MIDDLE  ALT=\"%28pi%29%28r%5E2%29%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The height h is fixed at 10.  The problem asks for the rate of change of volume with respect to diameter; so we need the volume equation in terms of the diameter:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28%28d%2F2%29%5E2%29%2810%29+=+%285pi%2F4%29%28d%5E2%29 ALIGN=MIDDLE  ALT=\"%28pi%29%28%28d%2F2%29%5E2%29%2810%29+=+%285pi%2F4%29%28d%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then dV/dd is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285pi%2F2%29%28d%29 ALIGN=MIDDLE  ALT=\"%285pi%2F2%29%28d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When the radius is 5, the diameter is 10, so when the radius is 5 the rate of change of volume with respect to diameter is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285pi%2F2%29%2810%29+=+25pi ALIGN=MIDDLE  ALT=\"%285pi%2F2%29%2810%29+=+25pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );