A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm

A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?

  1. 24
  2. 12
  3. 16
  4. 8

Answer 

A side of big cube of 12 cm is cut into smaller cube of side 3 cm. So, one side of big cube equals 4 sides of smaller cube.

The big cube is cut into 4 x 4 x 4 = 64 small cubes.

There are 8 original corners - 3 painted sides 

There are 12 edges on the original cube, each will give two cubes with two painted sides - 24 in all

There were 6 faces, each with four cubes with one painted side - 24 in all

So, the number with no painted sides is 64 - 8 - 24 - 24 = 8

The correct option is D.