A cubical box has each edge 10 cm. Find the length of longest rod which can be put into the box.

Answer

To find the length of the longest rod that can fit inside a cubical box with each edge measuring 10 cm, we can use the concept of the space diagonal of the cube. The space diagonal is the longest diagonal that can be drawn within the cube, connecting two opposite corners.

### Step-by-Step Solution:

1. **Identify the dimensions of the cube**:
- Each edge of the cube is given as 10 cm.

2. **Formula for the space diagonal of a cube**:
- The formula to calculate the length of the space diagonal \(d\) of a cube with edge length \(a\) is:
\[ d = a\sqrt{3} \]

3. **Substitute the edge length into the formula**:
- Here, \(a = 10 \, \text{cm}\).
- Therefore, substituting the value into the formula gives:
\[ d = 10 \sqrt{3} \]

4. **Calculate the numerical value**:
- To find the approximate length, we can use the value of \(\sqrt{3} \approx 1.732\):
\[ d = 10 \times 1.732 = 17.32 \, \text{cm} \]

5. **Conclusion**:
- The length of the longest rod that can be put into the box is approximately \(17.32 \, \text{cm}\).