document.write( "Question 1205029: A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
\n" ); document.write( "Calculate the rise in the water level if the original depth of water was:
\n" ); document.write( "a) 10cm
\n" ); document.write( "b) 2cm
\n" ); document.write( "(leave your answers in fractional form) \n" ); document.write( "

Algebra.Com's Answer #841634 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
\n" ); document.write( "Calculate the rise in the water level if the original depth of water was:
\n" ); document.write( "a) 10cm
\n" ); document.write( "b) 2cm
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\n" ); document.write( "\n" ); document.write( "        Regarding this problem and its solution in the post by @mananth, I'd like to make two notices.\r
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\n" ); document.write( "\n" ); document.write( "        First notice to (1) is that the solution by @mananth is correct ONLY IF the cylindrical tank\r
\n" ); document.write( "\n" ); document.write( "        has enough height in order for the displaced water does not flow out of the cylinder.\r
\n" ); document.write( "\n" ); document.write( "        Otherwise, the rise in the water level will be limited by the height of the cylinder.\r
\n" ); document.write( "\n" ); document.write( "        The problem says nothing about it, and it is the problem's FAULT.\r
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\n" ); document.write( "\n" ); document.write( "        Second notice is that the solution by @mananth for part 2) is FATALLY INCORRECT. \r
\n" ); document.write( "\n" ); document.write( "        See my correct solution below.\r
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\n" ); document.write( "\n" ); document.write( "                                Solution to part 2\r
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document.write( "The original volume of the water in the tank is  =  = 307.87582 cm^3.\r\n" );
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document.write( "The area of the horizontal section of the tank, occupied by the water after placing the solid cube\r\n" );
document.write( "is   =  = 89.93791 cm^2.\r\n" );
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document.write( "The final level of the water is then   = 3.423204075 cm,  or 3.423 cm after rounding.\r\n" );
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document.write( "Thus the rise of the water level is the difference  3.423 - 2 = 1.423 cm.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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\n" ); document.write( "\n" ); document.write( "Again, the solution by @mananth for part 2) is CONCEPTUALLY INCORRECT,\r
\n" ); document.write( "\n" ); document.write( "since he/she incorrectly determines the volume of the displaced water,
\n" ); document.write( "which is of fundamental importance in this problem.\r
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