document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121706>Question 1121706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains 1090 ft3 of grain?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737688 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for the volume of a right circular cone is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "V = pi * r^2 * h / 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "V is the volume<BR>\n" );
document.write( "pi is equal to 3.141592654<BR>\n" );
document.write( "r is the radius<BR>\n" );
document.write( "h is the height\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that the volume is 1090 cubic feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes 1090 = pi * r^2 * h / 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that the diameter is always 3 times the height.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the radius is always half the length of the diameter, then the radius is always 1.5 times the height.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace r with 1.5 * h in the formula and the formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1090 = pi * (1.5 * h)^2 * h / 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes 1090 = pi * 1.5^2 * h^2 * h / 3 which then becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1090 = pi * 2.25 * h^3 / 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by (2.25 * pi) and multiply both sides of this equation by 3 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1090 * 3) / (2.25 * pi) = h^3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for h^3 to get h^3 = 462.6103679.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for h to get h = cube root of that = 7.734016969 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the radius is 1.5 times the height, then the radius is equal to 11.60102545 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the diameter is 2 times the length of the radius, then the diameter is equal to 23.20205091 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to see if this is correct, replace the radius with 11.60102545 feet and replace the height with 7.734016969 feet and solve for the volume.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you will get V = pi * 11.60102545^2 * 11.60102545 / 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for V to get V = 1090.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the pile 7.73 feet high when the volume is 1090 cubic feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );