Question

The question is based on a solid cube which has been shaded as shown on pairs of opposite faces.

How many small cubes are there which have shading only on two faces?

• A. 8
• B. 9
• C. 12
• D. 16

Answer 1

The correct option is C 12

No. of cubes have shading on only two face$=(n-2)\times 12$
$=(3-2)\times 12=12$.

Since the cube has been shaded on opposite faces with same pattern.

The side cubes except the corner cubes are shaded on two faces.

So, for the top and bottom surface, there are 8 cubes shaded on two faces only.

And for front and back surfaces, the 4 cubes are shaded on two faces only.

So, total there are 12 cubes with shading on two faces.

Hence, option C is correct.