A hall has the dimensions 10m `xx` 10m `xx` 10 m. A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its displacement is nearly

Options

A. `5sqrt(3)m`
B. `10sqrt(3)m`
C. `20sqrt(3)m`
D. `30sqrt(3)m`

Answer

To find the magnitude of the displacement of the fly that starts at one corner of a cube and ends at the diagonally opposite corner, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Dimensions of the Cube**:
The hall is a cube with dimensions 10 m x 10 m x 10 m. This means each side of the cube is 10 meters long.

2. **Identify the Initial and Final Points**:
The fly starts at one corner of the cube, which we can denote as point A (0, 0, 0) and ends at the diagonally opposite corner, point B (10, 10, 10).

3. **Use the Displacement Formula**:
Displacement is the straight-line distance between the initial and final positions. We can calculate this using the 3D distance formula:
\[ \text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
Here, (x1, y1, z1) = (0, 0, 0) and (x2, y2, z2) = (10, 10, 10).

4. **Substitute the Coordinates into the Formula**:
\[ \text{Displacement} = \sqrt{(10 - 0)^2 + (10 - 0)^2 + (10 - 0)^2} \]
\[ = \sqrt{10^2 + 10^2 + 10^2} \]
\[ = \sqrt{100 + 100 + 100} \]
\[ = \sqrt{300} \]

5. **Simplify the Expression**:
\[ = \sqrt{100 \times 3} = 10\sqrt{3} \]

6. **Final Result**:
The magnitude of the displacement of the fly is \( 10\sqrt{3} \) meters.