SOLUTION: 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?

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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?
Answer by ikleyn(52772) About Me  (Show Source):
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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?
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We have six basic faces 8*12 (two), 8*16 (two) and 12*16 (two).


Small cubes that are painted on just one side, are those cubes that have one small face 
on the basic surfaces listed above, one strip away from their edges.


So, the numbers of such small cubes is 

    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.    


ANSWER.  The number of such small cubes is 568.

Solved.