Question

The six faces of a wooden cube of side 6 cm are labelled A, B, C, D, E and F respectively. Three of these faces A, B, and C are each adjacent to the other two, and are painted red. The other three faces are not painted. Then, the wooden cube is neatly cut into 216 little cubes of equal size. How many of the little cubes have no sides painted?

A.
125
B.
135
C.
91
D.
108
E.
100

Accepted Answer

A. The 3 painted faces are adjacent, meeting at a common corner. Removing the layer corresponding to each painted face leaves an unpainted inner sub-cube of size $(6-1) 	imes (6-1) 	imes (6-1) = 5 	imes 5 	imes 5 = 125$ cubes. Thus, 125 little cubes have no sides painted.

Painted Wooden Cube Cutting

Explanation

Practise this under exam conditions