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The problem describes a cube \(PQRS.TUVW\) with a side length of \(6 \, \text{cm}\). We need to find the distance between points \(P\) and \(W\).

### Solution:
1. **Visualize the Cube**:
   - \(P\) is at one vertex of the cube.
   - \(W\) is at the vertex diagonally opposite to \(P\) across the entire cube.

2. **Apply the 3D Diagonal Formula**:
   The formula to calculate the space diagonal \(d\) of a cube is:
   \[
   d = \sqrt{3} \cdot a
   \]
   where \(a\) is the side length of the cube.

3. **Substitute the Values**:
   \[
   a = 6 \, \text{cm}
   \]
   \[
   d = \sqrt{3} \cdot 6 \, \text{cm} = 6\sqrt{3} \, \text{cm}
   \]

4. **Calculate the Numerical Value**:
   If you need an approximate decimal value:
   \[
   6\sqrt{3} \approx 6 \times 1.732 \approx 10.39 \, \text{cm}
   \]

So, the distance between point \(P\) and point \(W\) is \(6\sqrt{3} \, \text{cm}\) or approximately \(10.39 \, \text{cm}\).

Would you like more details or have any other questions? Here are some related questions to consider:

1. How do you derive the formula for the space diagonal of a cube?
2. What would be the distance between two adjacent vertices of the cube?
3. How does the distance between the cube's vertices change if the side length is doubled?
4. Can you use the Pythagorean theorem to find the distance between two vertices in a cube?
5. What are some real-life applications of calculating distances in 3D objects?

**Tip:** In a cube, the space diagonal is always \(\sqrt{3}\) times the side length. This is a quick way to find such distances!

Diketahui kubus PQRS.TUVW dengan panjang rusuk 6 cm. Jarak antara titik P ke titik W adalah?

Learn how to calculate the distance between two opposite vertices of a cube with a side length of 6 cm. This geometry problem covers key concepts such as the space diagonal formula and the application of the Pythagorean theorem in 3D. Suitable for students in Grades 9-10.

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