document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866755>Question 866755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hollow container consists of a cylinder with a cone on top \r<BR>\n" );
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document.write( "The container contains oil up to the level of the top of the cylinder. the container is then turned upside down. Find the depth of the oil \r<BR>\n" );
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document.write( "Hight of cylinder = 6cm <BR>\n" );
document.write( "width = 8cm \r<BR>\n" );
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document.write( "and hight of cone = 4cm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522496 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=522496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> volume of the cylinder is equal to pi * r^2 * h<BR>\n" );
document.write( "h = 6 = height of cylinder.<BR>\n" );
document.write( "d = 8 = diameter of cylinder.<BR>\n" );
document.write( "r = 1/2 * 8 = 4 = radius of base of cylinder.<BR>\n" );
document.write( "v = pi * 4^2 * 6 = 96 * pi = 301.5928947.\r<BR>\n" );
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document.write( "volume of the cone is equal to 1/3 * pi * r^2 * h<BR>\n" );
document.write( "h = 4 = height of the cone.<BR>\n" );
document.write( "r = 4 = radius of the base of the cone.<BR>\n" );
document.write( "v = 1/3 * pi * 4^2 * 4 = 64/3 * pi = 67.02064328.\r<BR>\n" );
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document.write( "when you invert the cylinder, the oil rushes into the cone and fills it up.\r<BR>\n" );
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document.write( "Since the volume of the cylinder is larger than the volume of the cone, there will be oil left over after the cone is full.\r<BR>\n" );
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document.write( "that left over oil goes into the cylinder.\r<BR>\n" );
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document.write( "the volume of oil that is left over is equal to 301.5928947 - 67.02064328 which is equal to 234.5722515.\r<BR>\n" );
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document.write( "this is the volume of oil that is now in the cylinder.\r<BR>\n" );
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document.write( "the equation for the volume of the cylinder is:\r<BR>\n" );
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document.write( "v = pi * r^2 * h\r<BR>\n" );
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document.write( "pi stays the same at 3.141592654 and r stays the same at 4.<BR>\n" );
document.write( "v becomes 234.5722515 which is the volume of the oil that is now in the cylinder.\r<BR>\n" );
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document.write( "since v = 234.5722515 and r = 4, the formula for the cylinder becomes:\r<BR>\n" );
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document.write( "234.5722515 = pi * 4^2 * h\r<BR>\n" );
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document.write( "you want to solve for h.\r<BR>\n" );
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document.write( "you get h = 234.5722515 / (16*pi).\r<BR>\n" );
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document.write( "solve for h to get:\r<BR>\n" );
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document.write( "h = 4.6666..... which is equal to 4 2/3.\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "confirm by adding up the volume in the cone and the volume in the cylinder.\r<BR>\n" );
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document.write( "volume in the cone is equal to (1/3) * pi * 4^2 * 4 = 67.02064328<BR>\n" );
document.write( "volume in the cylinder is equal to pi * 4^2 * 4.6666... = 234.5722515<BR>\n" );
document.write( "total volume in cone and cylinder is equal to 301.5928947.\r<BR>\n" );
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document.write( "since this is the original volume of the oil in the cylinder before you turned the cylinder upside down, the value of h = 4 and 2/3 is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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