Page 72 - NUMINO Challenge_D2
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Basic Concepts The Number of Colored Faces
All the faces of the large cube shown on the right are
colored. The large cube is divided into 27 small cubes so
that 54 faces of the small cubes are colored.
The following table shows the number of small cubes
according to the number of colored faces they have.
Number of Colored 0 1 2 3
Faces
Location of Small Center of the large Center of the face Center of the edge Vertices
Cubes cube
8
Number of 1 6 12
Small Cubes
Example All the faces of the large cube on the right are
colored. Find the number of small cubes that
have zero, one, two, and three colored faces,
respectively.
Class Notes
The cubes that have zero colored faces are located at the center of the
cube as shown on the right. Therefore, the number of cubes that have
zero colored faces is 2 2 .
The cubes that have one colored face are located at the center of the
face, and there are four cubes in each face. Therefore the number of
cubes that have one colored face is 4 .
The cubes that have two colored faces are located at the center of the
edge, and there are two cubes on each edge. Therefore, the number of
cubes that have two colored faces is 2 .
The cubes that have three colored faces are located at the vertices.
Therefore, the number of cubes that have three colored faces is .
69Geometry
All the faces of the large cube shown on the right are
colored. The large cube is divided into 27 small cubes so
that 54 faces of the small cubes are colored.
The following table shows the number of small cubes
according to the number of colored faces they have.
Number of Colored 0 1 2 3
Faces
Location of Small Center of the large Center of the face Center of the edge Vertices
Cubes cube
8
Number of 1 6 12
Small Cubes
Example All the faces of the large cube on the right are
colored. Find the number of small cubes that
have zero, one, two, and three colored faces,
respectively.
Class Notes
The cubes that have zero colored faces are located at the center of the
cube as shown on the right. Therefore, the number of cubes that have
zero colored faces is 2 2 .
The cubes that have one colored face are located at the center of the
face, and there are four cubes in each face. Therefore the number of
cubes that have one colored face is 4 .
The cubes that have two colored faces are located at the center of the
edge, and there are two cubes on each edge. Therefore, the number of
cubes that have two colored faces is 2 .
The cubes that have three colored faces are located at the vertices.
Therefore, the number of cubes that have three colored faces is .
69Geometry
