2023 · Q46
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?
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- AIt is equal to the surface area of the large cube.
- BIt is less than the surface area of the large cube.
- CIt is more than the surface area of the large cube.
- DInsufficient data
Explanation
Each removed 2-cm cube had contributed one 4 cm^2 face to the outer surface, but its removal opens a pit exposing five faces totalling 20 cm^2, a net gain of 16 cm^2 per cube. The four cubes lie along a face diagonal and touch one another only at edges, so no pit walls are shared. The total gain is 64 cm^2 over the original 384 cm^2, so the surface area is more than that of the intact large cube. Hence option C.