Page 64 - NUMINO Challenge_C1

Basic Concepts Slicing Colored Cubes vertex

When you color the surface of a cube and cut it edge
into 27 smaller cubes of equal size, the cubes with face
three colored faces are those at the vertex. The
cubes with two colored faces are those at the
edge. The cubes with one colored face are those
on the face of the larger cube.

Example The cube on the right is colored and cut along
the lines into 27 identical cubes. Find the number
of cubes that have zero, one, two, and three
colored faces, respectively.

Class Notes

The cubes with three colored faces are all at the of the

larger cube, so there are cube(s) in all.

The cubes with two colored faces are all at the edges of the

larger cube, at each edge. Since there are edges,

there are small cubes with two colored faces.

There is (are) small cube(s) with a colored face on each of

the larger cube. Since there are faces on a cube, there are

small cubes with one colored face.

The number of small cubes with no colored faces is equal to the total number of cubes
subtracted by the number of cubes with colored faces.

Therefore, ( ).

Try It Again The surface of this rectangular prism is colored
and the prism is cut into small cubes. How
many cubes have two colored faces?

61Geometry