Question 10

A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?

Solution

Total number of cubes will be = $$\frac{12 \times 12 \times 12}{3 \times 3 \times 3}$$ = 64
Cubes with 3 sides painted = cubes at corner sides = 8
Cubes with 2 sides painted = cubes on lines = 24
Cubes with 1 sides painted = cubes on middle of surface = 24
So cubes with no side painted = 64 - (8+24+24) = 8

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