The area of the region covered by the TV broadcast by a TV tower of 100 m height is (Radius of the earth = `6.4 xx 10^6` m )

Options

A. `12.8 pi xx 10^8 km^(2) `
B. ` 1.28 pi xx 10^(3) km^(2) `
C. ` 0.64 pi xx 10^(3) km^(2) `
D. ` 1.28 xx 10^(3) km^(2) `

Explanation

To find the area of the region covered by the TV broadcast from a TV tower of height 100 m, we can use the formula for the area covered by a broadcast tower:

### Step-by-Step Solution:

1. **Identify the given values:**
- Height of the TV tower (h) = 100 m
- Radius of the Earth (R) = \(6.4 \times 10^6\) m

2. **Use the formula for the area covered by the broadcast:**
The area (A) covered by the TV broadcast can be approximated using the formula:
\[ A = 2 \pi h R \]

3. **Substitute the values into the formula:**
\[ A = 2 \pi (100) (6.4 \times 10^6) \]

4. **Calculate the area:**
- First, calculate \(2 \times 100 = 200\).
- Now, substitute this back into the equation:
\[ A = 200 \pi (6.4 \times 10^6) \]
- Next, calculate \(200 \times 6.4 = 1280\).
- Therefore, we have:
\[ A = 1280 \pi \times 10^6 \text{ m}^2 \]

5. **Approximate the value of \(\pi\):**
- Using \(\pi \approx 3.14\):
\[ A \approx 1280 \times 3.14 \times 10^6 \text{ m}^2 \]
- Calculate \(1280 \times 3.14 = 4027.2\):
\[ A \approx 4027.2 \times 10^6 \text{ m}^2 \]

6. **Convert the area from square meters to square kilometers:**
- Since \(1 \text{ km}^2 = 10^6 \text{ m}^2\):
\[ A \approx \frac{4027.2 \times 10^6}{10^6} \text{ km}^2 = 4027.2 \text{ km}^2 \]

7. **Final answer:**
- The area covered by the TV broadcast is approximately:
\[ A \approx 4.0272 \times 10^3 \text{ km}^2 \text{ or } 4027.2 \text{ km}^2 \]