a cube with each edge 3units long is painted on all its faces It is then cut into cubes - Maths - Understanding Elementary Shapes

Question

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

Shruti Tyagi · Accepted Answer

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

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5944edf97436f%20jpg"
style="width: 340px; height: 148px;">
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,

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