document.write( "Question 1015275: If a cube has an edge equal to the diagonal of another cube. Find the ratio of their volumes \n" ); document.write( "
Algebra.Com's Answer #631660 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's solution above is incorrect.\r\n" );
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document.write( "Let x be the length of every edge of the smaller cube.\r\n" );
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document.write( "ΔABC and ΔBCE are right triangles. (They don't look it \r\n" );
document.write( "because they're drawn in perspective to make a 2D drawing \r\n" );
document.write( "look like 3D.)  But ∠ACB is the right angle in right \r\n" );
document.write( "triangle ΔABC, and ∠BCE is the right angle in right\r\n" );
document.write( "triangle ΔBCE.\r\n" );
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document.write( "BC is the hypotenuse of right triangle ΔABC, and it is\r\n" );
document.write( "also the bottom leg of triangle ABC,\r\n" );
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document.write( "Using the Pythagorean theorem on right triangle ΔABC:\r\n" );
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document.write( "\"AB%5E2%2BAC%5E2=BC%5E2\"\r\n" );
document.write( "\"x%5E2%2Bx%5E2=BC%5E2\"\r\n" );
document.write( "\"2x%5E2=BC%5E2\"\r\n" );
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document.write( "Using the Pythagorean theorem on right triangle ΔABC:\r\n" );
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document.write( "\"BC%5E2%2BCE%5E2=BE%5E2\"\r\n" );
document.write( "\"2x%5E2%2Bx%5E2=d%5E2\"\r\n" );
document.write( "\"3x%5E2=d%5E2\"\r\n" );
document.write( "\"sqrt%283x%5E2%29=d\"\r\n" );
document.write( "\"x%2Asqrt%283%29=d\"\r\n" );
document.write( "\"x=d%2Fsqrt%283%29\"\r\n" );
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document.write( "Using the volume of a cube formula for the smaller cube: \r\n" );
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document.write( "\"V+=+edge%5E3\"\r\n" );
document.write( "\"V+=+x%5E3\"\r\n" );
document.write( "\"V+=+%28d%2Fsqrt%283%29%29%5E3\"\r\n" );
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document.write( "Using the volume of a cube formula for the larger cube:\r\n" );
document.write( "\"V+=+edge%5E3\"\r\n" );
document.write( "\"V+=+d%5E3\"\r\n" );
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document.write( "The ratio of the volume of the larger cube to the volume\r\n" );
document.write( "of the smaller cube:\r\n" );
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document.write( "\"matrix%281%2C3%2Cd%5E3%2C%22%3A%22%2C%28d%2Fsqrt%283%29%29%5E3%29\"\r\n" );
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document.write( "or the fraction:\r\n" );
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document.write( "\"d%5E3%2F%28d%2Fsqrt%283%29%29%5E3%29\"\"%22%22=%22%22\"\"d%5E3%2F%28%28d%5E3%2Fsqrt%283%29%5E3%29%29%29\"\"%22%22=%22%22\"\"d%5E3\"\"%22%22%2A%22%22\"\"%28%28sqrt%283%29%5E3%29%2Fd%5E3%29%29\"\"%22%22=%22%22\"\"sqrt%283%29%5E3\" to 1\r\n" );
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document.write( "So the volume of the larger cube is \"sqrt%283%29%5E3\" or about 5.2 times\r\n" );
document.write( "the volume of the smaller cube.\r\n" );
document.write( "Edwin
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