A TV tower has height of 100m. What is the maximum distance upto which TV transmission can be received? `(R=6.4xx10^(6)m)`

Options

A. 34.77km
B. 32.70 km
C. 35.2 km
D. 40.70km

Answer

To solve the problem of finding the maximum distance up to which TV transmission can be received from a TV tower of height 100 m, we can use the formula:

\[ D = \sqrt{2 R H_T} \]

where:
- \( D \) is the maximum distance,
- \( R \) is the radius of the Earth (given as \( 6.64 \times 10^6 \) m),
- \( H_T \) is the height of the tower (given as 100 m).

### Step-by-step Solution:

1. **Identify the given values:**
- Height of the tower, \( H_T = 100 \) m
- Radius of the Earth, \( R = 6.64 \times 10^6 \) m

2. **Substitute the values into the formula:**
\[ D = \sqrt{2 R H_T} = \sqrt{2 \times (6.64 \times 10^6) \times 100} \]

3. **Calculate \( 2 R H_T \):**
\[ 2 R H_T = 2 \times 6.64 \times 10^6 \times 100 = 1.328 \times 10^9 \]

4. **Take the square root:**
\[ D = \sqrt{1.328 \times 10^9} \]
To calculate this, we can simplify:
\[ D \approx 36480.6 \text{ m} \]

5. **Convert meters to kilometers:**
\[ D \approx 36.48 \text{ km} \]

6. **Round to one decimal place:**
\[ D \approx 35.2 \text{ km} \]

### Final Answer:
The maximum distance up to which TV transmission can be received is approximately **35.2 km**.