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The problem involves a cube where each edge has a length of 6 cm. We are asked to find the distances between specific points in the cube. Let's analyze each option:

1. **A ke F**: Points A and F are on different edges of the cube. Using the Pythagorean theorem for the diagonal of a face (AF), the distance can be found. 
   
   \[
   AF = \sqrt{AB^2 + BF^2} = \sqrt{6^2 + 6^2} = \sqrt{72} = 6\sqrt{2} \, \text{cm}
   \]

2. **B ke G**: This involves finding the space diagonal from B to G. The formula for a space diagonal in a cube is:
   
   \[
   d = \sqrt{AB^2 + BF^2 + BG^2} = \sqrt{6^2 + 6^2 + 6^2} = \sqrt{108} = 6\sqrt{3} \, \text{cm}
   \]

3. **A ke G**: This is also a space diagonal from A to G. Since the cube's space diagonal formula is:
   
   \[
   AG = \sqrt{6^2 + 6^2 + 6^2} = \sqrt{108} = 6\sqrt{3} \, \text{cm}
   \]

4. **A ke P**: A to P is a face diagonal. The distance can be calculated similarly to the A to F case, but on a different face.
   
   \[
   AP = \sqrt{6^2 + 6^2} = \sqrt{72} = 6\sqrt{2} \, \text{cm}
   \]

5. **O ke B**: O is the center of the cube, and B is a vertex. The distance from the center to a vertex is half the space diagonal, so:
   
   \[
   OB = \frac{6\sqrt{3}}{2} = 3\sqrt{3} \, \text{cm}
   \]

### Answer for each option:
- **A ke F** = \(6\sqrt{2}\) cm
- **B ke G** = \(6\sqrt{3}\) cm
- **A ke G** = \(6\sqrt{3}\) cm
- **A ke P** = \(6\sqrt{2}\) cm
- **O ke B** = \(3\sqrt{3}\) cm

Let me know if you'd like further details or have any questions!

### Related Questions:
1. What is the distance between point A and point E?
2. How do you calculate the space diagonal of any cube with a side length \(s\)?
3. What is the formula for the diagonal of a square face?
4. If the side length of the cube is doubled, how would the space diagonal change?
5. How does the Pythagorean theorem apply in 3D geometry?

### Tip:
In any cube, the diagonal across the face is always \(s\sqrt{2}\), and the space diagonal is \(s\sqrt{3}\), where \(s\) is the length of the edge.

Tentukan jarak titik di bawah ini jika panjang rusuknya adalah 6 cm. a. A ke F, b. B ke G, c. A ke G, d. A ke P, e. O ke B

Learn how to calculate the distances between various points in a cube with 6 cm edge length using the Pythagorean theorem. This includes face diagonals and space diagonals, suitable for students in Grades 8-10.

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