document.write( "Question 1114815: Two spheres of equal radius are taken out by cutting from a solid cube of side 13cm. What is the maximum volume(in cm^3) of each sphere. \n" ); document.write( "
Algebra.Com's Answer #729745 by ikleyn(52794)\"\" \"About 
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document.write( "I read and interpret the condition by different way: two spherical solids are taken out by cutting from a solid cube\r\n" );
document.write( "in a way that their centers are located on the  3D  (=longest) diagonal of the cube.\r\n" );
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document.write( "        (This condition provides the maximum radius and maximum volume to each of the two spheres).\r\n" );
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document.write( "Then it is clear that these spheres touch each other at the middle of the  3D  diagonal of the cube.\r\n" );
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document.write( "The length of the longest 3D diagonal of this cube is   \"13%2Asqrt%283%29\" cm.\r\n" );
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document.write( "If \"r\" is the radius of the sphere, then    \"r%2Asqrt%283%29%2Br\" = \"6.5%2Asqrt%283%29\" cm.\r\n" );
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document.write( "Hence,    r = \"%286.5%2Asqrt%283%29%29%2F%281+%2B+sqrt%283%29%29\" = 4.12 cm.\r\n" );
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document.write( "Then the volume of each sphere    V = \"%284%2F3%29%2Api%2Ar%5E3\" = \"%284%2F3%29%2A3.14%2A4.12%5E3\" = 292.8 cm^3.\r\n" );
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