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Question

All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes. How many small cubes will be formed having no face coloured ?

A
27
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B
8
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C
16
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D
24
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Solution

The correct option is C 27
The answer is option A
When the painted cube is cute into 125 small equal cubes, we have:
  • A 3 faces painted cube on every corner
Number of cubes with 3 face painted=1×8=8
  • Three 2-faces painted cube on every edge
  • Number of cubes with 2 face painted=3×12=36
      • Nine single face painted cube on side
      Number of cubes with 1 face painted=9×6=54
        Number of cubes with no face painted=12583654=27

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