Cube problem on test Imagine a 3 times 3 cube arrangement th

Cube problem on test: Imagine a 3 times 3 cube arrangement that is dipped in paint. There are how many 1 times 1 cubes in this arrangement? How many 1 times 1 cubes have exactly 3 faces painted? Describe their location. How many 1 times 1 cubes have exactly 2 faces painted? Describe their location. How many 1 times 1 cubes have exactly 1 faces painted? Describe their location. How many 1 times 1 cubes have exactly 0 faces painted? Describe their location.

Solution

In a 3 x 3 x 3 cube there are: Total of 27 cubes
1 cube with 0 sides painted.
6 cubes with 1 side painted.
12 cubes with 2 sides painted.
8 cubes with 3 sides painted.