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A block 7 cubes long, 5 cubes deep and 3 cubes high is painted on all six faces and cut up. How many small cubes have no paint?

Competition practiceDice & Cubes

A35
B105
C24
D15

Step-by-Step Solution

Remove one layer from every face:

(7 - 2) \times (5 - 2) \times (3 - 2) = 5 \times 3 \times 1 = 15

. (35 forgets to remove the layers from the height.)

Answer: D) 15

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