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 231458: 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 Theo(13342) About Me  (Show Source):
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27 cubes glued together to form a larger cube.

The big cube is formed from 3 little cubes on each side.

3 * 3 * 3 = 27 little cubes.

There is 1 cube in the middle with no faces exposed.
There are 8 cubes on the corners with 3 faces exposed.
There are 12 cubes on the edges with 2 faces exposed.
There are 6 cubes in the middle of each side of the big cube that have only 1 face exposed.

All the exposed faces have been painted pink.

The product of the number of cubes with 1 pink face and the number of cubes with 3 pink faces would be:

8 * 6 = 48