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 given data
- Height of the TV tower (h) = 70 m
- Average population density (ρ) = 1000 people/km²
- Radius of the Earth (R) = 6.4 × 10^6 m

### Step 2: Convert population density to m²
Since the population density is given in km², we need to convert it to m²:
1 km² = (1000 m)² = 10^6 m²
Thus, the population density in people/m² is:
\[ \rho = \frac{1000 \text{ people}}{10^6 \text{ m}^2} = 10^{-3} \text{ people/m}^2 \]

### Step 3: Calculate the distance (d) covered by the broadcast
We can use the formula for the distance covered by the broadcast:
\[ d = \sqrt{2hR} \]
Substituting the values:
\[ d = \sqrt{2 \times 70 \, \text{m} \times 6.4 \times 10^6 \, \text{m}} \]
Calculating this:
\[ d = \sqrt{2 \times 70 \times 6.4 \times 10^6} \]
\[ d = \sqrt{8960000} \approx 2993.33 \, \text{m} \]

### Step 4: Calculate the area covered by the broadcast
The area (A) covered by the broadcast can be calculated using the formula for the area of a circle:
\[ A = \pi d^2 \]
Substituting the value of d:
\[ A = \pi (2993.33)^2 \]
Calculating this:
\[ A \approx 3.14 \times 8960000 \approx 28134400 \, \text{m}^2 \]

### Step 5: Calculate the population covered
Now, we can find the total population covered by multiplying the area by the population density:
\[ \text{Population} = \rho \times A \]
Substituting the values:
\[ \text{Population} = 10^{-3} \, \text{people/m}^2 \times 28134400 \, \text{m}^2 \]
Calculating this:
\[ \text{Population} \approx 28134.4 \, \text{people} \]

### Final Answer
The population covered by the TV broadcast is approximately **28134 people**.

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