The length of the longest rod that can fit in a cubical vessel of side 10 cm, is

Options

A. 10 cm
B. 20 cm
C. `10 sqrt2 cm`
D. `10 sqrt3 cm`

Explanation

To find the length of the longest rod that can fit inside a cubical vessel, we need to determine the space diagonal of the cube. The formula for the space diagonal \(d\) of a cube with side length \(a\) is given by:

\[ d = a\sqrt{3} \]

### Step-by-Step Solution:

1. **Identify the side length of the cube**:
The side length \(a\) of the cubical vessel is given as 10 cm.

2. **Substitute the side length into the formula**:
We will substitute \(a = 10\) cm into the diagonal formula.

\[ d = 10\sqrt{3} \]

3. **Calculate the value of \(\sqrt{3}\)**:
The approximate value of \(\sqrt{3}\) is about 1.732.

4. **Multiply to find the diagonal**:
Now, we will multiply:

\[ d = 10 \times 1.732 = 17.32 \text{ cm} \]

5. **Final Answer**:
The length of the longest rod that can fit in the cubical vessel is approximately 17.32 cm.