Directions (1 of 3 questions): A cube of 5 cm has been painted on its surfaces in such a...
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Directions (1 of 3 questions):**
A cube of 5 cm has been painted on its surfaces in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red. Two remaining surfaces have been left unpainted. Now the cube is cut into smaller cubes of side 1 cm each.
How many cubes will have no side painted?
Show answer & explanation
The interior core contains 3x3x3 = 27 unpainted cubes. The two unpainted adjacent outer faces contain 21 additional unpainted cubes, totaling 27 + 21 = 48 cubes with no side painted.
Step-by-step Derivation:
Step 1: Inner core of a 5x5x5 cube has size 3 x 3 x 3 = 27 cubes.
Step 2: The cube has 2 unpainted adjacent faces. Each 5x5 unpainted face adds 3x3 = 9 cubes not touching painted sides.
Step 3: The edge where the two unpainted faces meet contributes 3 more unpainted cubes.
Step 4: Total unpainted cubes = 27 + 9 + 9 + 3 = 48.