Group QuestionAnswer the following question based on the information given below.Two opposite sides of a cube are painted red. Two of the other opposite sides of the cube are painted green. The remaining sides are painted blue.Q.If the cube is subdivided into 216 smaller cubes, then how many smaller cubes will have its faces coloured with green and blue both, but not red?a)16b)12c)18d)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

216 = 6³
Each surface of the cube is cut into 36 smaller squares.
As shown, there are only 4 edges that are common to green and blue.
On each of the 4 edges, there are 4 cubes that are painted with only green and blue.
The number of cubes that have only green and blue on their surfaces is 16.
Hence, option 1.

Answer

If the cube divides into 216 smaller ones. Then it will have 6*6 cubes on each side. The green and blue cubes will be both in the edges of the cube. So there will be 4 edges which has painted both green and blue.
6*4=24,but in the corners red painted cubes will also be there (8 corners). Therefore 24-8=16 cubes were painted with both green and blue but not red.

Answer

To solve this problem, we need to understand the structure of the cube and how it is subdivided into smaller cubes.

Structure of the cube:
A cube has 6 faces, 12 edges, and 8 vertices. Opposite faces of a cube have the same color. In this case, two opposite sides are painted red, and two opposite sides are painted green. The remaining sides are painted blue.

Subdivision of the cube:
The cube is subdivided into smaller cubes. Each face of the original cube is divided into smaller squares, resulting in a total of 6 x 6 = 36 smaller squares on the faces of the original cube. Each smaller square represents a smaller cube.

Now, let's analyze the given information to determine the number of smaller cubes that have their faces colored with green and blue, but not red.

Analysis:
1. Green and blue faces:
- Each face of the original cube has 6 smaller squares.
- Two opposite faces are painted green, which means there are a total of 6 x 2 = 12 smaller squares that are green.
- The remaining faces are painted blue, which means there are a total of 6 x 2 = 12 smaller squares that are blue.

2. Overlapping squares:
- Two smaller squares on the original cube can be seen from two different sides. These overlapping squares have two colors on their faces.
- In this case, the overlapping squares will have one green face and one blue face.

Now, let's calculate the number of smaller cubes with green and blue faces, but not red.

Calculation:
- The total number of smaller squares on the faces of the original cube is 6 x 6 = 36.
- Out of these, 12 are green, 12 are blue, and the remaining 36 - 12 - 12 = 12 squares are red.
- Each smaller square represents a smaller cube.
- So, the number of smaller cubes with green and blue faces, but not red, is 12.

Therefore, the correct answer is option 'A' - 16 smaller cubes will have their faces colored with green and blue, but not red.

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