A T.V tower is 150 m tall. If the area around the tower has a population density of `750" km"^(-2)`, then the population covered by the broadcasting tower is about , (Re = 6400 km)

Options

A. `4.5xx10^(6)`
B. `2.5xx10^(6)`
C. `4.5xx10^(5)`
D. `2.5xx10^(5)`

Answer

To solve the problem, we need to find the population covered by a broadcasting tower given its height, the population density in the area, and the radius around the tower.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Height of the tower (h) = 150 m
- Population density (ρ) = 750 people/km²
- Radius (R) = 6400 km

2. **Convert Height to Kilometers:**
- Since the radius is given in kilometers, we need to convert the height of the tower from meters to kilometers.
\[ h = 150 \, \text{m} = \frac{150}{1000} \, \text{km} = 0.15 \, \text{km} \]

3. **Calculate the Area Covered by the Tower:**
- The area (A) covered by the tower can be calculated using the formula for the surface area of a cylinder (considering the height of the tower):
\[ A = 2 \pi R h \]
- Substituting the values:
\[ A = 2 \times \pi \times 6400 \, \text{km} \times 0.15 \, \text{km} \]
- Using \(\pi \approx 3.14\):
\[ A \approx 2 \times 3.14 \times 6400 \times 0.15 \]
\[ A \approx 2 \times 3.14 \times 6400 \times 0.15 \approx 602.4 \times 6400 \approx 38400 \, \text{km}^2 \]

4. **Calculate the Total Population Covered:**
- The total population (P) covered by the broadcasting tower can be calculated using the formula:
\[ P = \text{Population Density} \times \text{Area} \]
- Substituting the values:
\[ P = 750 \, \text{people/km}^2 \times 38400 \, \text{km}^2 \]
\[ P = 750 \times 38400 = 28800000 \, \text{people} \]

5. **Final Result:**
- The population covered by the broadcasting tower is approximately **28,800,000 people**.