Question

Some cubes equal in size have been arranged in the form of a solid block as shown in the figure below. All the faces of this solid block except the bottom one have been coloured yellow.
How many cubes are not coloured on any face?

• A. 6
• B. 9
• C. 12
• D. 15

Answer 1

Answer: (D)

15

Consider this cube layer by layer.
$1^{st}$ layer from bottom.
Number of uncolored cubes= Total number of cubes- colored cubes
=$20-14=6$
$2^{nd}$ layer from bottom.
Number of uncolored cubes= Total number of cubes- colored cubes
= $20-14=6$
$3^{rd}$ layer from bottom.
Number of uncolored cubes= Total number of cubes- colored cubes
= $19-16=3$
$4^{th}$ layer from bottom.
Number of uncolored cubes= Total number of cubes- colored cubes
= $12-12=0$
Total number of uncolored cubes= $6+6+3+0=15$