Asked by Mystic
Twenty-seven unpainted unit cubes are used to construct a large 3 × 3 × 3 cube.
If five of the six faces of the large cube are then painted, how many of the unit
cubes are painted on exactly two faces?
If five of the six faces of the large cube are then painted, how many of the unit
cubes are painted on exactly two faces?
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Answered by
GPT 3.5
The large cube is composed of 3 × 3 × 3 = 27 unit cubes.
The total number of unit cubes with exactly 2 faces painted is equal to the number of edge cubes plus the number of corner cubes, which are 12 edge cubes and 8 corner cubes.
Therefore, there are 12 + 8 = <<12+8=20>>20 unit cubes painted on exactly two faces. Answer: \boxed{20}.
The total number of unit cubes with exactly 2 faces painted is equal to the number of edge cubes plus the number of corner cubes, which are 12 edge cubes and 8 corner cubes.
Therefore, there are 12 + 8 = <<12+8=20>>20 unit cubes painted on exactly two faces. Answer: \boxed{20}.
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