Algebra.Com's Answer #811607 by ikleyn(52786)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "four grapefruit (considered spheres) 6 in. in diameter are placed in a square box
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document.write( "whose inside base dimensions are 12 in. in the space between the first 4 grapefruit
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document.write( "a fifth of the same diameter is placed. how deep must the box be so that the top
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document.write( "will just touch the fifth grapefruit.
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document.write( "(a) The centers of the first 4 spheres are vertices of a square with the side length of 2*3 = 6 inches.\r\n" );
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document.write( "(b) The diagonal of this square is  inches long.\r\n" );
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document.write( " The half of this diagonal is  inches long .\r\n" );
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document.write( "(c) Now consider the right angled triangle formed by the centers of the 1st and 5th spheres as the hypotenuse,\r\n" );
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document.write( " vertical line from the center of the 5th spere as the leg, \r\n" );
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document.write( " and the horizontal line from the center of the 1st sphere coinciding with the diagonal of the above mentioned square.\r\n" );
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document.write( "(d) The hypotenuse of this triangle is 2 times the radius of 3 cm, i.e. 6 inches.\r\n" );
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document.write( " Its leg, parallel to the diagonal of the square, is inches long.\r\n" );
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document.write( " Having it, you just can calculate the length of the vertical leg. It is\r\n" );
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document.write( "  =  =  = .\r\n" );
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document.write( " ( It is interesting to note, that it MEANS that the line connecting centers of the 1st and the 5th square\r\n" );
document.write( " is inlined 45 degrees to horizon (!) )\r\n" );
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document.write( "(e) Thus we found that the center of the 5th sphere is elevated inches over the plane of the centers \r\n" );
document.write( " of the first four spheres.\r\n" );
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document.write( "(f) Combining the gained information, we see that the depth of the box must be equal to \r\n" );
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document.write( "  =  inches = 10.243 inches (rounded).\r\n" );
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document.write( "ANSWER. The depth of the box should be equal to inches = 10.243 inches (rounded).\r\n" );
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document.write( "Solved, answered and carefully explained.\r
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