Question

A cube is painted red along all its faces and then divided into 27 smaller identical pieces. How many of the resultant pieces will have no face painted?

• A. 3
• B. 1
• C. 9
• D. 2

Answer 1

The correct option is B

1

The cuboid can be cut into 27 smaller identical pieces by applying 2 cuts parallel to each face of the cube, hence will be having 3 layers of pieces, the front and back layer would be painted, similarly top and bottom layer, left side and right side layer would be painted, so number of layer of no face painted pieces would be (3-2) x (3-2) x (3-2) = 1 x 1 x 1 = 1 piece.