Nisha has glued 27 small cubes together to make a large solid cube. She paints the large cube red. How many of the original small cubes have— (a) three faces painted red? (b) two faces painted red? (c) one face painted red? (d) no faces painted red?
8 small cubes have three faces painted red.
12 small cubes have two faces painted red.
6 small cubes have one face painted red.
1 small cube has no faces painted red.
Explanation
(a) The corner cubes of a ×3 cube have 3 faces exposed to the outside, so they get painted on 3 faces. (b) The edge cubes (not corners) have 2 faces exposed. A cube has 12 edges, and each edge has 1 middle cube. (c) The face center cubes have only 1 face exposed. A cube has 6 faces, and each face has 1 center cube. (d) Only the very center cube is completely hidden inside, with no faces exposed to the outside.