A block of wood 10 cm long, 6 cm wide and 4 cm high is painted on every face and then cut into cubes of edge 2 cm. How many of these cubes have exactly one painted face?

Question

Accepted Answer

6. Cutting into 2 cm cubes gives 5×3×2 cubes. The block is only 2 cubes high, so the cubes with one painted face lie in the top or bottom layer away from all four sides: (5-2)×(3-2)=3 in each layer, 2×3=6.

A block of wood 10 cm long, 6 cm wide and 4 cm high is painted on every face and then cut into cubes of edge 2 cm. How many of these cubes have exactly one painted face?

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