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. 8
• C. 16
• D. 24

Answer 1

Answer: (A)

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

$\Rightarrow \text{Number of cubes with 3 face painted}=1\times 8=8$

• Three 2-faces painted cube on every edge
$\Rightarrow \text{Number of cubes with 2 face painted}=3\times 12=36$
• Nine single face painted cube on side
$\Rightarrow \text{Number of cubes with 1 face painted}=9\times 6=54$

$\therefore$ Number of cubes with no face painted$=125-8-36-54=27$