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Sixty-four cubes of sides 2 cm each are combined to form a cube of side 8 cm. If four of the smaller cubes along the diagonal of a surface are removed from the surface of the large cube, which one of the following statements about the surface area of this solid object is true?
Explanation
The large cube of side 8 cm is composed of 64 smaller cubes of side 2 cm. When a small cube is removed from the surface, the change in surface area depends on its position. Removing a corner cube removes three original faces but exposes three new internal faces, leaving the total surface area unchanged. Removing an edge cube (not a corner) removes two original faces but exposes four new ones, increasing the area. Removing a face-center cube removes one face but exposes five new ones, also increasing the area. In this specific case, four cubes are removed along a surface diagonal. This diagonal includes two corner cubes and two edge cubes. For the corner cubes, the area remains the same. For the edge cubes, the area actually increases. However, standard geometric logic for this specific problem type often assumes the removal of cubes that do not overlap in a way that reduces the net exposed area, resulting in an area that is equal to or greater than the original.