Page 153 - NUMINO Challenge_C1
P. 153
Answer
Key
Geometry Problem solving
7 Rectangular Prisms and Cubes p.60~p.61 1 The three faces that meet at a vertex of a cube
Example cannot be opposite faces to one another.
Switzerland meets France, Japan, Germany, and
Try It Again USA at a vertex, therefore its opposite face is
Australia. Germany meets Switzerland, USA,
Australia, and France at a vertex, therefore its
opposite face is Japan. France is the opposite
face to USA.
(Switzerland, Australia), (Germany, Japan),
(France, USA)
2
Example vertex, 8
1, 12, 12
1, face, 6, 6 Type 7-2 Slicing Colored Cubes p.64~p.65
27, 8, 12, 6, 1
TryItAgain The number of long edges is equal to the 1 There are eight vertices in a cube. Therefore,
number of the cubes with two colored faces. there are eight small cubes with three colored
Therefore, there are four cubes. faces.
Type 7-1 Finding Opposite Faces in Cubes p.62~p.63 2 The cube has 12 edges, and each edge has 3
small cubes with two colored faces. Therefore,
1 B, C, D, and F meet with A at a vertex. there are 12 3 36 small cubes with two
Therefore, E is the opposite face to A. colored faces.
2 A, B, D, and E meet with C at a vertex. 3 The cube has 6 faces, and each face has 9 small
Therefore, face F is the opposite face to C. cubes with one colored face. Therefore, there
are 6 9 54 small cubes with one colored face.
3 (A, E), (C, F), and (B, D) are opposite faces each
other. Therefore, D is the opposite face to B. 4 When you subtract the number of cubes with at
least one colored face from 125 (the total
number of small cubes), you get 125 8 36
54 27 as the number of small cubes with no
colored faces.
NUMINO Challenge C1
Key
Geometry Problem solving
7 Rectangular Prisms and Cubes p.60~p.61 1 The three faces that meet at a vertex of a cube
Example cannot be opposite faces to one another.
Switzerland meets France, Japan, Germany, and
Try It Again USA at a vertex, therefore its opposite face is
Australia. Germany meets Switzerland, USA,
Australia, and France at a vertex, therefore its
opposite face is Japan. France is the opposite
face to USA.
(Switzerland, Australia), (Germany, Japan),
(France, USA)
2
Example vertex, 8
1, 12, 12
1, face, 6, 6 Type 7-2 Slicing Colored Cubes p.64~p.65
27, 8, 12, 6, 1
TryItAgain The number of long edges is equal to the 1 There are eight vertices in a cube. Therefore,
number of the cubes with two colored faces. there are eight small cubes with three colored
Therefore, there are four cubes. faces.
Type 7-1 Finding Opposite Faces in Cubes p.62~p.63 2 The cube has 12 edges, and each edge has 3
small cubes with two colored faces. Therefore,
1 B, C, D, and F meet with A at a vertex. there are 12 3 36 small cubes with two
Therefore, E is the opposite face to A. colored faces.
2 A, B, D, and E meet with C at a vertex. 3 The cube has 6 faces, and each face has 9 small
Therefore, face F is the opposite face to C. cubes with one colored face. Therefore, there
are 6 9 54 small cubes with one colored face.
3 (A, E), (C, F), and (B, D) are opposite faces each
other. Therefore, D is the opposite face to B. 4 When you subtract the number of cubes with at
least one colored face from 125 (the total
number of small cubes), you get 125 8 36
54 27 as the number of small cubes with no
colored faces.
NUMINO Challenge C1
