Question

a cube is painted red on two adjacent sides and black on the focus opposite to the red faces and green on the remaining faces is cut into 64 small cubes of equal size. how many cubes have only one face painted​

Answer 1

Answer:

The larger cube is cut into 64 smaller cubes. This implies that the edge of a smaller cube is one-fourth that of the larger cube. We know that the two adjacent faces are painted red and the two faces opposite to these faces are painted black. This implies that the top and the bottom faces are painted green. Thus, there are two edges where the faces painted red and black meet, and each edge has four cubes. Thus, there are totally 88 smaller cubes on each face. So, there are 32 smaller cubes which have at least one of their faces green. The remaining 64 - 32 = 32 smaller cubes have none of their faces green.