document.write( "Question 1208389: The water in a hemi-spherical bowl is 42 cm across the top is 9 cm deep. How much more water is needed to fill the bowl to the brim?
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Algebra.Com's Answer #846808 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The water in a hemi-spherical bowl is 42 cm across the top $\"highlight%28cross%28is%29%29\"$ and 9 cm deep.
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\n" ); document.write( "\n" ); document.write( "        In his post, Edwin instructs to use the radius of the sphere R = 21 cm.\r
\n" ); document.write( "\n" ); document.write( "        It is a strategic error. It shows that Edwin misread the problem.\r
\n" ); document.write( "\n" ); document.write( "        The radius of the sphere is not given in this problem.\r
\n" ); document.write( "\n" ); document.write( "        In this problem, \"42 cm across the top\" means \"42 cm across the water surface\".\r
\n" ); document.write( "\n" ); document.write( "        Finding the hemi-sphere radius is the first step of the solution.\r
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document.write( "If you make a sketch, you will see a right angled triangle.\r\n" );
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document.write( "Its hypotenuse is the radius of the sphere R.\r\n" );
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document.write( "Its legs are  (R-9) cm and 42/2 = 21 cm.\r\n" );
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document.write( "So, we write the Pythagorean equation\r\n" );
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document.write( "    (R-9)^2 + 21^2 = R^2.\r\n" );
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document.write( "From it, we find\r\n" );
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document.write( "    R^2 - 18R + 81 + 441 = R^2,\r\n" );
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document.write( "    81 + 441 = 18R\r\n" );
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document.write( "    18R = 522\r\n" );
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document.write( "      R = 522/18 = 29.\r\n" );
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document.write( "Thus the sphere radius is 29 cm.\r\n" );
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document.write( "Then we find the volume of the hemi-sphere\r\n" );
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document.write( "     =  =  = 51080.202 cm^3.\r\n" );
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document.write( "Next you find the volume of the spherical segment for R = 29 cm and h = 9 cm\r\n" );
document.write( "using the formula\r\n" );
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document.write( "     =  =  = 6616.194 cm^3.\r\n" );
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document.write( "Now your answer is the difference of the two volumes\r\n" );
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document.write( "     -  = 51080.202 - 6616.194 = 44464.008 cm^3,  or 44.464 liters  (rounded).\r\n" );
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