a cube with each edge 3units long is painted on all its faces. It is then cut into cubes with edges 1 unit long. Find the number of smaller cubes that will have paint on 0 surface, 1 surface, 2 surfaces and 3 surfaces

Dear Student,


The following diagram shows the 3 possible scenarios when a cube of side 3 units is divided into smaller cubes of 1 unit.



So as we can see the number of cubes having 3 faces painted= 8 (pink coloured cubes)
Cubes with 2 faces painted= 12 (blue coloured cubes)
Cubes with 1 face coloured- 6  (1 on each face)
Cubes with 0 faces coloured =1 ( the cube in the centre of all sides)

Regards,


 

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