document.write( "Question 1125926: The problem goes as follows: Two metal balls are placed in a cylinder containing water. The lower has a radius of 7cm and the upper has a radius of 3cm. The diameter of the cylinder is 18cm. The total volume of water in the cylinder is 2414/3 x Pi cm3. The volume of water that has to be poured out so that there is just enough water to cover both balls? \n" ); document.write( "

Algebra.Com's Answer #742350 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " It is very good problem for someone who wants to check how creative is his (or her) mind in solving problems
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document.write( "There are two basic stable configurations for the spherical balls in this cylinder.\r\n" );
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document.write( "One configuration is shown in the Figure on the right.\r\n" );
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document.write( "The larger ball lies at the bottom of the cylinder and touches the cylinder's vertical lateral surface.   \r\n" );
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document.write( "The smaller ball is above the bottom. It touches the larger ball and also touches vertical lateral \r\n" );
document.write( "surface of the cylinder.\r\n" );
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document.write( "The Figure shows a vertical section of the cylinder and the two balls by that existing and unique \r\n" );
document.write( "vertical plane which contains the cylinder's vertical axis and the centers of the two balls.\r\n" );
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document.write( "In the Figure, you see a right angled triangle shown in red.\r\n" );
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document.write( "The hypotenuse of this triangle is the segment AB connecting the centers of balls.\r\n" );
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document.write( "This segment goes through the tangent point, and its length is  7 + 3 = 10 cm.\r\n" );
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document.write( "You can easily find the horizontal leg of this triangle, x.\r\n" );
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document.write( "From the equation  7 + x + 3 = 18  you have  x = 18 - 7 - 3 = 8.\r\n" );
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document.write( "Then the vertical leg of this triangle is   =  = 6 cm.\r\n" );
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document.write( "Thus the height of the highest point of the small ball over the cylinder bottom is  7 + 6 + 3 = 16 centimeters.\r\n" );
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document.write( "It defines the minimal required upper level of 16 cm of the water in the cylinder after submerging the balls.\r\n" );
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document.write( "With it, the volume equation is\r\n" );
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document.write( " = W +   + ,   or\r\n" );
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document.write( "W =  -  =  =  = \r\n" );
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document.write( "where W is the minimal required volume of the water before submerging the balls.\r\n" );
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document.write( "Now, how much of water has to be poured out so that there is just enough water to cover both balls? - It is the difference \r\n" );
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document.write( "     cm^3  MINUS   cm^3 =  cm^3 =  cm^3.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The other stable configuration is when the small ball lies on the bottom, while the larger ball leans on it.\r
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