document.write( "Question 1183282: when a cube is completely submerged in a cylindrical jar of radius 3.5 cm containing water to a height of 8 cm, the water level rises by 4mm.calculate the length of one side of the cube correct to 4 significant figure \n" ); document.write( "

Algebra.Com's Answer #813517 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "When a cube is completely submerged in a cylindrical jar of radius 3.5 cm containing water to a height of 8 cm,
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document.write( "The volume of the cube is equal to the difference of the occupied volumes in the cylinder after and before submerging.\r\n" );
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document.write( "This difference of volumes is   =  = 15.393791 cm^3.\r\n" );
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document.write( "In the formula, the value 0.4 represents the water level rise expressed in centimeters.\r\n" );
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document.write( "So, if the length of the cube' side is \"a\", then you have this equation to find \"a\"\r\n" );
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document.write( "    a^3 = 15.393791,\r\n" );
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document.write( "which gives the solution  a =  = 2.4876 cm.\r\n" );
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document.write( "We only need to check that the diagonal of the cube's face is less than the cylinder's diameter.\r\n" );
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document.write( "The diagonal is   = 3.5180 cm, which is less than the diameter of 2*3.5 = 7 cm.\r\n" );
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document.write( "ANSWER.  The side of the cube is  2.4876 cm.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The basic idea of the solution is that the volume of the submerged body is the difference of occupied volumes.\r
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\n" ); document.write( "\n" ); document.write( "This fact is known from the Archimedes era.\r
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\n" ); document.write( "\n" ); document.write( "        About Archimedes, read from these Internet sources\r
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\n" ); document.write( "\n" ); document.write( "                https://en.wikipedia.org/wiki/Archimedes\r
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\n" ); document.write( "\n" ); document.write( "                http://archimedespalimpsest.org/about/history/archimedes.php\r
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\n" ); document.write( "\n" ); document.write( "                http://www.ancientgreece.com/s/People/Archimedes/\r
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\n" ); document.write( "\n" ); document.write( "        It is really interesting reading (!)\r
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar and different solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Water level rise in a tank after submerging bodies \r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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