A TV tower has a height of 75m. What is the maximum area upto which this TV communication can be possible ?

Options

A. 1509 km^2
B. 3018 km^2
C. 2254 km^2
D. 6036 km^2

Answer

To find the maximum area up to which a TV communication can be possible from a tower of height 75 meters, we can use the formula for the area covered by the signals:

### Step-by-Step Solution:

1. **Understand the Formula**: The area \( A \) that can be covered by the signals from a tower is given by the formula:
\[ A = 2 \pi r h \]
where:
- \( r \) is the radius of the Earth,
- \( h \) is the height of the tower.

2. **Convert the Height**: The height of the tower is given as 75 meters. We need to convert this height into kilometers for consistency with the radius of the Earth.
\[ h = 75 \, \text{meters} = 75 \times 10^{-3} \, \text{km} = 0.075 \, \text{km} \]

3. **Use the Radius of the Earth**: The average radius of the Earth is approximately 6400 km. Thus, we have:
\[ r = 6400 \, \text{km} \]

4. **Substitute the Values into the Formula**: Now we can substitute the values of \( r \) and \( h \) into the area formula:
\[ A = 2 \pi (6400) (0.075) \]

5. **Calculate the Area**: We can use \( \pi \approx 3.14 \) for our calculations:
\[ A = 2 \times 3.14 \times 6400 \times 0.075 \]
\[ A = 2 \times 3.14 \times 6400 \times 0.075 = 2 \times 3.14 \times 480 = 3014.4 \, \text{km}^2 \]

6. **Final Result**: The maximum area up to which TV communication can be possible is approximately:
\[ A \approx 3018 \, \text{km}^2 \]

### Conclusion:
The maximum area up to which this TV communication can be possible is approximately **3018 km²**.