Question

A cube whose two adjacent faces are coloured is cut into $64$ identical small cubes. How many of those small cubes are not coloured at all?

• A. $24$
• B. $32$
• C. $36$
• D. $48$

Answer 1

The correct option is A $24$

The cube is coloured on two adjacent faces(let's take that sides as top and back surfaces).

So, the cubes on the surface having no colour will be

$12$ cubes on the front surface.

$6,6$ cubes on right and left surface and $4$ cubes at the bottom surface.

So, total cubes on the surface with no colour are $12+6+6+4=28$.

The small cubes which are enclosed in the big cube are only $8$ and they won't have a colour.

Thus, the total no. of cubes with no colour$=28+8=36$.

Hence, option C is correct.