How many of these cubes are painted blue?

Question

If you had a box that was 8 cm by 5 cm by 2 cm and was painted blue and cut into 80 cubes, each with dimensions of 1 cm. How many of these cubes are painted blue on exactly one face?

 

 

Answer 1

Imagine a rectangular box with dimensions of 2 cm, 5 cm, and 8 cm. Now the only ones that get blue paint on only one face are the ones that are not on any of the edges. There are only two such faces, and they measure 8 by 5. But you still need to not count the ones that are on the edge. This reduces the area to 6 by 3. Please realize that you need to subtract one from each of right, left, up, and down. This yields 18 such cubes. There are two such faces, so the answer is 36.