Question

Some equal cubes are arranged in the form of a solid block as shown in the adjacent figure. All the visible surfaces of the block (except the bottom) are then painted.

How many cubes have only two faces painted ?

• A. 0
• B. 16
• C. 20
• D. 24

Answer 1

The correct option is D 24

In 1st row from bottom, number of cubes have only two faces painted = corner cubes = 4
In 2nd row from bottom, number of cubes have only two faces painted = corner cubes = 4
In 3rd row from bottom, number of cubes have only two faces painted = corner cubes + top open side cubes - top opened corner cube = 4 + 2 - 1 = 5
In 4th row from bottom, number of cubes have only two faces painted = corner cubes = 5
In 5th row from bottom, number of cubes have only two faces painted = total cube - corner cubes - only top open cube = 12 - 5 - 1 = 6
Then total cube whose only two faces painted = 4 + 4 + 5 + 5 + 6 = 24.

Hence, option D is correct.