T.V. tower has a height of 70 m. How much population is covered by the TV broadcast average population density around the tower is `1000 km^(-2)` Radius of the earth is `6. 4 xx10 ^(6)`m.

Answer

To solve the problem of how much population is covered by the TV broadcast from a tower of height 70 m, we will follow these steps:

### Step 1: Understand the problem
We need to find the area covered by the TV broadcast and then calculate the population based on the given population density.

### Step 2: Calculate the effective radius of coverage
The effective radius (d) of the broadcast can be calculated using the Pythagorean theorem. The formula for the distance to the horizon from a height \( h \) above the Earth's surface is given by:
\[ d = \sqrt{(R + h)^2 - R^2} \]
where \( R \) is the radius of the Earth and \( h \) is the height of the tower.

### Step 3: Substitute the values
Given:
- Height of the tower, \( h = 70 \) m
- Radius of the Earth, \( R = 6.4 \times 10^6 \) m

Substituting these values into the formula:
\[ d = \sqrt{(6.4 \times 10^6 + 70)^2 - (6.4 \times 10^6)^2} \]

### Step 4: Simplify the expression
Since \( h \) is very small compared to \( R \), we can use the approximation:
\[ d \approx \sqrt{2Rh} \]
Substituting the values:
\[ d \approx \sqrt{2 \times (6.4 \times 10^6) \times 70} \]

### Step 5: Calculate the distance
Calculating the above expression:
\[ d \approx \sqrt{2 \times 6.4 \times 70 \times 10^6} = \sqrt{896000000} \approx 2993.33 \text{ m} \]

### Step 6: Calculate the area of coverage
The area \( A \) covered by the broadcast is given by the formula:
\[ A = \pi d^2 \]
Substituting the value of \( d \):
\[ A \approx \pi (2993.33)^2 \]

### Step 7: Calculate the area
Calculating the area:
\[ A \approx 3.14 \times (2993.33)^2 \approx 3.14 \times 8960000 \approx 28160000 \text{ m}^2 \]

### Step 8: Convert area to km²
To convert from m² to km²:
\[ A \approx \frac{28160000}{1000000} \approx 28.16 \text{ km}^2 \]

### Step 9: Calculate the population covered
Given the population density is \( 1000 \text{ people/km}^2 \):
\[ \text{Population} = \text{Area} \times \text{Population Density} \]
\[ \text{Population} = 28.16 \times 1000 \approx 28160 \text{ people} \]

### Final Answer
The population covered by the TV broadcast is approximately **28160 people**.

---