document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678353>Question 678353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet. The oil begins draining at a constant rate of 2 cubic feet per second. [Hint: depth and volume are not the same]\r<BR>\n" );
document.write( "\n" );
document.write( "a) Write the volume of the oil remaining the tank t seconds later as a function of t.\r<BR>\n" );
document.write( "\n" );
document.write( "b) Write the depth of the oil remaining in the tank t seconds later as a function of t.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421355 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the original volume of the oil; (radius = 10 ft)<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A10%5E2%2A40 ALIGN=MIDDLE  ALT=\"pi%2A10%5E2%2A40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V = 12566.37 cu/ft of oil<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The oil begins draining at a constant rate of 2 cubic feet per second. [Hint: depth and volume are not the same]<BR>\n" );
document.write( "a) Write the volume of the oil remaining the tank t seconds later as a function of t.<BR>\n" );
document.write( "V = 12566.37 - 2t<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) Write the depth of the oil remaining in the tank t seconds later as a function of t.<BR>\n" );
document.write( "Find the depth (x) of 2 cu ft in this tank, let <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A10%5E2%2Ax ALIGN=MIDDLE  ALT=\"pi%2A10%5E2%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28%28100%2Api%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28%28100%2Api%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = .0063662 ft per second at a 2 cu/ft per second rate <BR>\n" );
document.write( "d = 40 - .0063662t<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can check this by finding how long it will take to empty the tank<BR>\n" );
document.write( "12566.37/2 = 6283.2 seconds<BR>\n" );
document.write( "Find the depth of oil drained in this time<BR>\n" );
document.write( "6283.2 * .0063662 = 40.00 ft </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );