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The problem involves a cube with a side length of 6 cm. We are asked to determine the distance between several pairs of points on the cube.

Let's analyze the distances for each pair:

1. **Distance from A to F**:  
   Points A and F are located on the same edge of the cube. The distance between A and F is the side length of the cube, which is 6 cm.

2. **Distance from B to G**:  
   Points B and G are located on the diagonal of one of the faces of the cube. To find the distance of the diagonal on a face, we use the Pythagorean theorem:
   \[
   \text{Diagonal} = \sqrt{6^2 + 6^2} = \sqrt{72} = 6\sqrt{2} \, \text{cm}
   \]

3. **Distance from A to G**:  
   Points A and G are diagonally opposite in the three-dimensional space of the cube. To calculate this distance, we use the 3D Pythagorean theorem:
   \[
   \text{Distance} = \sqrt{6^2 + 6^2 + 6^2} = \sqrt{108} = 6\sqrt{3} \, \text{cm}
   \]

4. **Distance from A to P**:  
   Points A and P are located along one of the edges of the cube. Since P is directly above A, the distance from A to P is simply the side length of the cube, which is 6 cm.

5. **Distance from O to B**:  
   The point O is the center of the cube. To find the distance from the center of the cube (O) to any vertex (B), we use half the diagonal of the cube:
   \[
   \text{Distance} = \frac{\sqrt{6^2 + 6^2 + 6^2}}{2} = \frac{\sqrt{108}}{2} = 3\sqrt{3} \, \text{cm}
   \]

### Answers:
- **a. A to F**: 6 cm
- **b. B to G**: \(6\sqrt{2}\) cm
- **c. A to G**: \(6\sqrt{3}\) cm
- **d. A to P**: 6 cm
- **e. O to B**: \(3\sqrt{3}\) cm

Would you like a further explanation of any of these points or do you have any questions?

### Additional Related Questions:
1. How do you calculate the diagonal of a cube face?
2. How is the 3D Pythagorean theorem applied in space?
3. What is the formula for the distance between two opposite vertices of a cube?
4. How do you find the center of a geometric shape like a cube?
5. What are other properties related to the diagonals of a cube?

**Tip**: To find distances in a 3D space, always use the Pythagorean theorem in three dimensions: \(\sqrt{x^2 + y^2 + z^2}\).

Tentukan jarak titik di bawah ini jika panjang rusuknya adalah 6 cm.

Learn how to calculate distances between points on a cube with a side length of 6 cm. This problem involves applying the Pythagorean theorem in 2D and 3D, and is suitable for students in Grades 8-10.

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