This cube has five cubes along each edge. The faces are covered, but the cube is hollow inside. Can it be divided into two pieces of equal volume? Explain.

I am not sure what this question is asking?

This question is asking whether a cube with a hollow interior, where the faces are covered, can be divided into two pieces of equal volume.

To analyze this situation, we need to consider the properties of a cube. A cube has six equal faces and all its edges are of equal length. In this case, the cube has five smaller cubes along each edge, indicating that the interior of the cube is hollow.

To determine if it can be divided into two pieces of equal volume, we need to examine possible dividing planes. If we were to cut the cube through the center into two identical halves, each half would have the same number of smaller cubes along each edge.

However, since the interior of the larger cube is hollow, cutting it through the center would result in one half having empty spaces inside, while the other half would have additional smaller cubes in its interior. This means the two pieces would not have equal volumes.

Thus, in this specific case, it is not possible to divide the cube into two pieces of equal volume.