document.write( "Question 1105589: A cake shaped like a rectangular prism with sides of 9cm by 14cm by 15cm is completely dipped in chocolate and then cut into small 1 cm3 cubes. How many of the cubes have chocolate on just one side? \n" ); document.write( "

Algebra.Com's Answer #720449 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A cake shaped like a rectangular prism with sides of 9cm by 14cm by 15cm is completely dipped in chocolate
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document.write( "According to the condition, the entire/(the whole) cake is cut into small (1 cm X 1 cm x 1 cm) cubes.\r\n" );
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document.write( "The total number of these small cubes is  9*14*15 = 1890.\r\n" );
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document.write( "Of them, have chocolate on at least one side those and only those cubes that are in one slice adjacent to some (to any) face of the prism.\r\n" );
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document.write( "The rest of the small cubes HAVE NO chocolate on any small faces.\r\n" );
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document.write( "Those small cubes that have no chocolate on any small face are ALL INTERNAL cubes.\r\n" );
document.write( "They form smaller prism whose dimensions are 2 cm less than dimensions of the whole prism. \r\n" );
document.write( "Namely, these dimensions are (9-2) = 7 cm, (14-2) = 12 cm  and (15-2) = 13 cm.\r\n" );
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document.write( "So, the number of small INTERNAL cubes is 7*12*13 = 1092.\r\n" );
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document.write( "Thus the number of cubes that have chocolate at least on one side is  1890 - 1092 = 798.\r\n" );
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document.write( "The number of small cubes that have chocolate exactly on one side is\r\n" );
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document.write( "2*(7*12 + 7*13 + 12*13) = 662.\r\n" );
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document.write( "Answer.    The number of small cubes that have chocolate at least on one side is  798.\r\n" );
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document.write( "           The number of small cubes that have chocolate exactly on one side is 662.\r\n" );
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