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 do not have any of the faces painted ?

• A. $27$
• B. $8$
• C. $10$
• D. $12$

Answer 1

The correct option is D $12$

Number of cubes, that do not have any of the faces painted in first layer from bottom = total cubes - cubes(have at-least one face visible) $=16-12=4$
Number of cubes, that do not have any of the faces painted in second layer from bottom = total cubes - cubes(have at-least one face visible) $=16-12=4$
Number of cubes, that do not have any of the faces painted in third layer from bottom = total cubes - cubes(have at-least one face visible) $=16-13=3$
Number of cubes, that do not have any of the faces painted in forth layer from bottom = total cubes - cubes(have at-least one face visible) $=16-15=1$
Then total number of cubes that do not have any of the faces painted $=4+4+3+1=12$.