Nisha has a large solid cube made from 27 small cubes. Since 3 × 3 × 3 = 27, the large cube is a 3 × 3 × 3 cube.
She paints the entire large cube red.
(a) The large solid cube has 8 corners small cubes, and each corner small cube is painted red.
So, 8 small cubes are three faces painted red.
(b) Since a cube has 12 edges or sides, and 1 cube in the middle of each edge is painted red.
So, there are 12 small cubes with two faces painted red.
(c) These are the small cubes located in the center of each face of the large cube. A cube has 6 faces. Each face of the large cube is a 3 × 3 square of small cubes. The center small cube of each 3 × 3 face has only one face exposed to the outside, or painted red. So, there are 6 small cubes with one face red.
(d) For a 3 × 3 × 3 = 27 cube, if we remove the outer layer of cubes, we are left with an inner cube. This means there is only 1 small cube right in the very center of the large cube that has no faces painted red.
= 1 hour)
