A cube with a side length of 5 inches is painted black on all six faces. The entire cube is then cut into smaller cubes with sides of 1 inch. How many small cubes do not have any paint on them?

Answer 1

The volume of a cube with edge lengths of 5 inches can be found by multiplying 5 x 5 x 5. To solve this problem you have to envision this three dimensional cube with each 5 inch edge divided into 1 inch pieces.

The only 1 inch cubes that with have no paint are those hidden inside the cube not touching any outside piece. Take each 5 inch dimension and subtract 2 inches to remove the outer cubes that will have paint on them. This results in (5-2) x (5-2) x (5-2) or 3 x 3 x 3 which equals 27.