document.write( "Question 1193210: Imagine that you have used centimeter cubes to build a larger cube with side length 4 centimeters. You then paint your large cube blue on every side. If you take your cube apart, how many of the small cubes will have
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\n" ); document.write( "\n" ); document.write( "Repeat question 1 for the cubes with side lengths of 1, 2, 3, and 5 centimeters. Be sure to organize your work, perhaps by using a table. \r
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\n" ); document.write( "outcome for n = 6. What about n = 100?
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Algebra.Com's Answer #825221 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "For  n x n x n  cube\r\n" );
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document.write( "    - the number of cubes that have 3 blue faces is 8   // the corner cubes;\r\n" );
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document.write( "    - the number of cubes having 2 blue faces is 12*(n-2)  // the cubes along 12 edges, without counting the corner cubes;\r\n" );
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document.write( "    - the number of cubes having 1 blue face  is n^3 - (n-2)^3 - 12*(n-2) - 8.\r\n" );
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document.write( "      In the last formula,  n^3 - (n-2)^2  is the number of all small cubes minus the number of interior cubes,\r\n" );
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document.write( "      that comprise the smaller (n-2)*(n-2)*n-2) cube;\r\n" );
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document.write( "      12*(n-2)  is the number of cubes along 12 edges that have two faces painted blue;\r\n" );
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document.write( "      and 8 is the number of corner cubes, having 3 faces painted blue.\r\n" );
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