A T.V. tower has a height `100 m`. What is the population density around the T.V. tower if the population density around the T.V. tower if the total population covered is `50 lakh` ? Radius of earth ` = 6.4 xx 10^(6) m`.

Answer

To find the population density around the T.V. tower, we can follow these steps:

### Step 1: Understand the problem
We need to calculate the population density around a T.V. tower that has a height of 100 meters, with a total population of 50 lakh (5 million) people.

### Step 2: Calculate the radius of coverage
The coverage radius (r) around the T.V. tower can be calculated using the formula:
\[ r = \sqrt{2 \cdot R \cdot h} \]
where:
- \( R \) is the radius of the Earth (6.4 × 10^6 m)
- \( h \) is the height of the T.V. tower (100 m)

Substituting the values:
\[ r = \sqrt{2 \cdot (6.4 \times 10^6) \cdot 100} \]
Calculating this:
\[ r = \sqrt{1.28 \times 10^8} \approx 11314.1 \text{ m} \]

### Step 3: Calculate the area of coverage
The area (A) covered by the T.V. tower can be calculated using the formula for the area of a circle:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi \cdot (11314.1)^2 \]
Calculating this:
\[ A \approx \pi \cdot 128,000,000 \approx 402,123,856.2 \text{ m}^2 \]

### Step 4: Calculate the population density
Population density (D) is defined as the total population divided by the area:
\[ D = \frac{\text{Total Population}}{\text{Area}} \]
Substituting the values:
\[ D = \frac{50 \times 10^5}{402,123,856.2} \]
Calculating this:
\[ D \approx \frac{5,000,000}{402,123,856.2} \approx 0.0124 \text{ people/m}^2 \]

### Final Answer
The population density around the T.V. tower is approximately **0.0124 people/m²**.

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