There is a 4-inch cube painted on all sides.
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There is a 4-inch cube painted on all sides. This is cut down into 1-inch cubes. What is the number of cubes which have no painted sides?
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Answer: B. B) 8
For an n-inch cube painted on all sides, the number of unpainted 1-inch cubes is (n-2)^3. For n = 4, (4 - 2)^3 = 2^3 = 8.
Step-by-step Derivation:
Step 1: A 4x4x4 cube has outer layer of thickness 1 painted on all 6 sides.
Step 2: The unpainted core has dimensions (4-2) x (4-2) x (4-2) = 2 x 2 x 2 = 8 cubes.