A TV tower has a height of `60 `m. What is the maximum distance and area up to which TV transmission can be received? (Take radius of earth as `6.4 xx 10^6 m`).

Explanation

To solve the problem of determining the maximum distance and area up to which TV transmission can be received from a TV tower of height 60 m, we will follow these steps:

### Step 1: Calculate the Maximum Distance
We can use the formula for the distance \( d \) from a tower, which is given by:
\[ d = \sqrt{2RH} \]
where:
- \( R \) is the radius of the Earth,
- \( H \) is the height of the tower.

Given:
- Height of the tower \( H = 60 \) m,
- Radius of the Earth \( R = 6.4 \times 10^6 \) m.

Substituting the values into the formula:
\[ d = \sqrt{2 \times (6.4 \times 10^6) \times 60} \]

Calculating the value:
1. Calculate \( 2 \times 6.4 \times 10^6 \):
\[ 2 \times 6.4 \times 10^6 = 12.8 \times 10^6 \]
2. Multiply by \( 60 \):
\[ 12.8 \times 10^6 \times 60 = 768 \times 10^6 \]
3. Now take the square root:
\[ d = \sqrt{768 \times 10^6} = 27.7 \text{ km} \]

### Step 2: Calculate the Area of Coverage
The area \( A \) covered by the transmission can be calculated using the formula:
\[ A = \pi d^2 \]
Substituting the distance we found:
\[ A = \pi (27.7)^2 \]

Calculating the area:
1. Calculate \( (27.7)^2 \):
\[ (27.7)^2 = 767.29 \]
2. Now multiply by \( \pi \) (using \( \pi \approx 3.14 \)):
\[ A = 3.14 \times 767.29 \approx 2411 \text{ km}^2 \]

### Final Answers
- Maximum distance of TV transmission: **27.7 km**
- Area of coverage: **2411 km²**

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