SSC CPO SI and ASI Model Paper 1

(4) When the cube of side 8 cm each is sliced into 1 $\mathit{c}{\mathit{m}}^3$ cubes, we will get 8 × 8 × 8 = 512 cubes, each of volume 1 cm3 In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.
Therefore, the cubeswhich are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted. In each face of the larger cube, there will be 8 × 8 = 64 cubes. Of these, there will be 28 cubes on the edge and 6 ×6 = 36 cubes which are not on the edge.
∴ At 1 face, there will be 36 cubes each of 1 cm3 that will have exactly one of their sides painted.
∴ Total number of cubes each of 1$\mathit{c}{\mathit{m}}^3$ that will have exactly one of their sides painted $=36\times 6=216$