A 3 × 3 × 3 cube is painted on all sides and then cut into 27 unit cub…

Question

A 3 × 3 × 3 cube is painted on all sides and then cut into 27 unit cubes. How many small cubes have EXACTLY 2 painted faces?

Accepted Answer

B. 12 cubes

For an n × n × n cube: edges = 12(n − 2).
For n = 3: 12 × 1 = 12 small cubes with exactly 2 painted faces.
(Corners = 8 with 3 faces; faces = 6 with 1; inside = 1 with 0.)

Answer

8 cubes

Answer

6 cubes

Answer

1 cube

A 3 × 3 × 3 cube is painted on all sides and then cut into 27 unit cubes. How many small cubes have EXACTLY 2 painted faces?

Keep practising Analogies