Question

A TV tower has a height of 100 m. How much population is covered by TV broadcast, if the average population density around the tower is \( 1000 \, {km}^{-2} \) (radius of Earth = \( 6.4 \times 10^6 \, {m} \))?

• A. \( 10^3 \)
• B. \( 10^6 \)
• C. \( 4 \times 10^6 \)
• D. \( 4 \times 10^9 \)

Hint:

To calculate the coverage area, use the height of the tower to find the radius of the coverage area, then multiply by the population density to find the total population covered.

Answer 1

The Correct Option is C

The area covered by the TV tower can be calculated using the formula for the area of a circle:

\[ A = \pi r^2 \] where \( r \) is the radius of the coverage area, which is the distance that the signal can travel from the tower. The radius \( r \) can be derived using the height of the tower and the Earth's radius, based on the geometry of the situation:

\[ r = \sqrt{2 h R} \] where \( h \) is the height of the tower (100 m) and \( R \) is the radius of the Earth (\( 6.4 \times 10^6 \, {m} \)). This relationship comes from the geometry of a line of sight between the tower and the Earth's curvature. By calculating this, we can find the radius \( r \).

The population covered is then given by multiplying the population density by the area:

\[ \text{Population} = \text{Population density} \times A \] After substituting the known values, we find the population covered to be approximately \( 4 \times 10^6 \).

Hence, the correct answer is (c).