Twenty seven small cubes are glued to make a big cube and the exterior is painted yellow. How many among each of the 27 small cubes would have been painted yellow on :
1. only one of its faces
2. two of its faces
3. three of its faces.
Please send an explanation to the answers
Only one of the pointed faces = marked by 1 = 1
Since, there are six such faces, so number of cubes with only one of its faces pointed = 6 × 1 = 6
cubes with 2 faces pointed are marked by 2.
Number of cubes with 2 faces pointed in top layer = 4
Number of cubes with 2 faces pointed in middle layer = 4
Number of cubes with 2 faces pointed in bottom layer = 4
So, number of cubes with 2 faces pointed = 4 + 4 + 4 = 12
Number of cubes with three of its faces pointed in top layer = 4.
Number of cubes with three of its faces pointed in bottom layer = 4
Number of cubes with three of its faces pointed in middle layer = 0
So, number of cubes with three of its faces pointed = 4 + 4 = 8
∴ 1. Only one of its faces = 6
2. Only two of its faces = 12
3. Three of its faces = 8