Question

A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into 64 smaller cubes of equal size. How many cubes have less than three faces painted?

(a) 0
(b) 16
(c) 32
(d) 48

Answer 1

The cube is divided into smaller cubes, and we need to determine the number of cubes that have less than three faces painted. The correct answer is (a) 0.

Step-by-step explanation:

To determine the number of cubes that have less than three faces painted, let's analyze the cube.

Each corner of the cube is shared by 8 smaller cubes, so it contributes to the painting of 1/8 of each smaller cube. Since there are 8 corners of the cube, there are a total of 8/8 = 1 smaller cube with all three faces painted.

Therefore, there are no smaller cubes with greater than or equal to 3 faces painted.

So the correct answer is (a) 0.