document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945165>Question 945165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylindrical tank 4.67 m in diameter is placed with its axis vertical and is partially filled with water. A spherical diving bell is then completely immersed in the tank, causing the water level to rise 1.00 m. Find the diameter of the diving bell.\r<BR>\n" );
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document.write( "Round the 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 #576329 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=576329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the cylinder has a diameter of 4.67 meters.<BR>\n" );
document.write( "this means it has a radius of 3.335 meters.<BR>\n" );
document.write( "when the diving bell is immersed in the tank, the water level goes up 1 meter.<BR>\n" );
document.write( "the volume of water displaced is therefore equal to the volume of a cylinder that has a diameter of 4.67 meters and a height of 1 meter.<BR>\n" );
document.write( "the volume would be equal to pi * r^2 * h which is equal to pi * 3.335^2 which is equal to 3.335^2 * pi.\r<BR>\n" );
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document.write( "the volume of a sphere is equal to 4/3 * pi * r^3.<BR>\n" );
document.write( "the radius of the sphere is not the same radius as the cylinder, however.<BR>\n" );
document.write( "the radius of the sphere is what we need to solve for.<BR>\n" );
document.write( "that sphere must have the same volume as the water that was displaced which is equal to pi * 3.335^2.\r<BR>\n" );
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document.write( "your equation becomes:<BR>\n" );
document.write( "volume of sphere is equal to the volume of the 1 meter high section of the cylinder.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "volume of sphere = 4/3 * pi * r^3 which is equal to the volume of the 1 inch high section of the cylinder which is equal to 3.335^2 * pi.<BR>\n" );
document.write( "the equation without all the words is\":<BR>\n" );
document.write( "4/3 * pi * r^3 = 3.335^2 * pi.\r<BR>\n" );
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document.write( "multiply both sides of this equation by 3/4 and divide both sides of this equation by pi to get r^3 = 3/4 * 3.335^2 * pi / pi.<BR>\n" );
document.write( "simplify to get r^3 = 8.34166875.<BR>\n" );
document.write( "solve for r to get r = 2.028076409.\r<BR>\n" );
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document.write( "the radius of the sphere is equal to 2.028076409.<BR>\n" );
document.write( "the volume of the sphere is equal to 4/3 * pi * 2.028076409^3 which is equal to 11.122225 * pi.<BR>\n" );
document.write( "the volume of the 1 inch high section of the cylinder is equal to 3.335^2 * pi which is equal to 11.122225 * pi.\r<BR>\n" );
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document.write( "the volume of the sphere is the same as the volume of the 1 meter high section of the cylinder.<BR>\n" );
document.write( "the diameter of the diving bell is the same as the diameter of the sphere (they are the same thing) which is 2 times the radius of the sphere which makes the diameter of the diving bell equal to 4.056152818 meters which is equal to 4.06 meters rounded to 2 decimal places.<BR>\n" );
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