SOLUTION: Twenty-seven congruent cubes are glued together to form a larger cube. All six faces of the larger cube are painted pink. What is the product of the number of small cubes that have

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Question 238729: Twenty-seven congruent cubes are glued together to form a larger cube. All six faces of the larger cube are painted pink. What is the product of the number of small cubes that have a single pink face and the number of small cubes that have three pink faces?
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
The way I would attack this problem is to actually draw the cube which comprises of 3 layers of 9 small cubes all together.
Then looking at the cube you can count the small cubes that have a one face painted and those that have three.
Looking at the larger cube you can see that the the middle smaller cube of each face of the larger cube has one face coloured. So that is 6 small cubes with 1 face.
The small cubes with three faces coloured are the corner ones of the larger face. So that is 8 cubes.
So the answer is 6*8 = 48.
There may be a more mathematical way of doing this that other tutors can elabourate on...
Does this help?