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
• B. 24
• C. 8
• D. 16

Answer 1

The correct option is A 27

Correct option is (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=125−8−36−54=27

Try to imagine the inner block of 3$\times$3$\times$3. Which is just inside the painted outer shell.