Question

How many smaller cubes have only one face painted black?

• A. 58
• B. 7
• C. 46
• D. 32
• E. None

Answer 1

The correct option is A 58

From the cube which is coloured black on all the faces, there will be 25 small cubes cut from each face. Out of these 25 cubes 9 cues lying in the middle will have only one face painted black. Thus, from the cube cut into 125 small cubes, there will be 54 total cubes which will have only one face painted black.
From the cube with only one face painted black is cut into 64 mall cubes. There will be only 4 such cubes from the face painted black which have only one of the faces black in colour.
Thus, total number of small cubes with black coloured face is 58