1. 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?
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By: anil on 05 May 2019 02.33 am
Total number of cubes will be = $$frac{12 imes 12 imes 12}{3 imes 3 imes 3}$$ = 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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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