document.write( "Question 1209433: A solid rectangular prism with sides of 8cm by 12cm by 16cm is painted brown and then cut into 1cm^3 cubes. How many of the small cubes are painted on just one side? \n" ); document.write( "

Algebra.Com's Answer #848821 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "A solid rectangular prism with sides of 8cm by 12cm by 16cm is painted brown
\n" ); document.write( "and then cut into 1cm^3 cubes. How many of the small cubes are painted on just one side?
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document.write( "We have six basic faces 8*12 (two), 8*16 (two) and 12*16 (two).\r\n" );
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document.write( "Small cubes that are painted on just one side, are those cubes that have one small face \r\n" );
document.write( "on the basic surfaces listed above, one strip away from their edges.\r\n" );
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document.write( "So, the numbers of such small cubes is \r\n" );
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document.write( "    2*(8-2)*(12-2) + 2*(8-2)*(16-2) + 2*(12-2)*(16-2) =  2*6*10 + 2*6*14 + 2*10*14 = 568.    \r\n" );
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document.write( "ANSWER.  The number of such small cubes is 568.\r\n" );
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