Question

A cube is cut into two equal parts along a plane parallel to one of it the faces. One piece is colored orange on the two largest faces and yellow on the remaining. The other piece is colored yellow on two smaller adjacent faces and orange on the remaining. Each is then cut into $32$ cubes of the same size. These $64$ cubes are mixed up. Then, how many cubes have only one colored face?

• A. $8$
• B. $16$
• C. $20$
• D. $24$

Answer 1

The correct option is B $16$

The bigger cube is made up of 4 layers each of which has 16 smaller cubes.

When the cube is cut in half, each piece will have 2 layers of 16 smaller cubes each.

Each layer of the two pieces has 4 smaller cubes with only one face exposed.

Therefore, there are 16 smaller cubes that has only one coloured face.

Option B is correct.