The area of the region covered by the TV., broadcast by a T.V. tower of height 100 m is (in `m^2`)

Options

A. `8.4pixx10^8`
B. `1.28pixx10^9`
C. `1.92pixx10^8`
D. `8.4pixx10^9`

Answer

To solve the problem of finding the area covered by a TV broadcast from a tower of height 100 m, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for Distance (D)**:
The distance (D) covered by the TV broadcast can be calculated using the formula:
\[ D = 2 \sqrt{R \cdot H_t} \]
where \( R \) is the radius of the Earth and \( H_t \) is the height of the tower.

2. **Use the Given Values**:
- Height of the tower (\( H_t \)) = 100 m
- Radius of the Earth (\( R \)) = 6400 km = \( 6400 \times 10^3 \) m = \( 6.4 \times 10^6 \) m

3. **Calculate the Distance (D)**:
Substitute the values into the formula:
\[ D = 2 \sqrt{(6.4 \times 10^6) \cdot 100} \]
\[ D = 2 \sqrt{6.4 \times 10^8} \]
\[ D = 2 \cdot 8 \times 10^4 = 16 \times 10^4 \text{ m} = 1.6 \times 10^5 \text{ m} \]

4. **Calculate the Area (A)**:
The area covered by the broadcast is given by:
\[ A = \pi D^2 \]
Substitute \( D \):
\[ A = \pi (1.6 \times 10^5)^2 \]
\[ A = \pi (2.56 \times 10^{10}) \text{ m}^2 \]
\[ A = 2.56 \pi \times 10^{10} \text{ m}^2 \]

5. **Final Result**:
The area covered by the TV broadcast is:
\[ A \approx 2.56 \pi \times 10^{10} \text{ m}^2 \]