A cube is painted red on all six outer faces and then sliced into 64 smaller identical unit cubes. How many of these unit cubes have exactly two painted faces?

Answer and explanation

Correct answer: D. 24 cubes

  1. Step 1: Determine dimensions of the cut cube: Total cubes = n^3 = 64 => n = 4.
  2. Step 2: Cubes with exactly two painted faces lie along the edges of the cube, excluding the corner cubes.
  3. Step 3: Each cube has 12 edges. Along each edge of length n, there are (n - 2) edge cubes with 2 painted faces.
  4. Step 4: Calculate: 12 (4 - 2) = 12 2 = 24 unit cubes.
Answer
24 cubes.
Why not the others: '12 cubes' assumes 1 cube per edge; '8 cubes' is the number of corner cubes with 3 painted faces; '16 cubes' calculates face-center cubes with 1 painted face (6 * (4-2)^2 = 24).

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