there are 27 small cubes arranged in a 3 by 3 by 3 cube. The top and sides of the cube are painted red. How many of the 27 small cubes have 0 faces painted? 1 face? 2 faces? 3 faces? 4 faces? 5 faces? 6 faces?

1 Face has 0 face painted

Step-by-step explanation:

As per the question a painted cube that is cut into 27 equal-size smaller cubes has been cut into a 3 * 3 * 3 arrangement.

There is 1 cube in the very center

On each of the 6 sides of the cube, there is a central smaller cube that is painted once.

Of the 27 (3*3*3) smaller cubes formed by the cutting, 1 gets no paint, 6 are painted on 1 face, 12 are painted on 2 faces, and 8 are painted on 3 faces (total 27 cubes).

1 (no paint) + 6 (painted 1) + 12 (painted 2) + 8 (painted 3) = 27 total

The sum of the painted faces (of the small cubes) is 54 (which is 6*9).