Multiple choice

A TV tower has a height of $75\ m$. The maximum distance and area up to which this TV transmission can be received is (Radius of the Earth = $6400\ km$)

  1. $31\ km$, $3018\ {km}^{2}$
  2. $30\ km$, $3000\ {km}^{2}$
  3. $28\ km$, $2800\ {km}^{2}$
  4. $25\ km$, $2500\ {km}^{2}$
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A Correct answer
Explanation

Distance d = sqrt(2Rh), where R = 6400 km and h = 0.075 km. d = sqrt(2 * 6400 * 0.075) = sqrt(960) approx 30.98 km. Area A = pi * d^2 = 3.14 * 960 approx 3014 sq km.

AI explanation

The maximum distance for TV transmission is found using the range formula d equals the square root of two times h times R, where h is the tower height and R is the earth's radius. Substituting 75 m for h and 6400 km for R gives d equals the square root of two times 0.075 times 6400, which simplifies to the square root of 960 and equals approximately 31 km. The coverage area is calculated using the formula area equals pi times d squared, so the area equals 3.1416 times 31 squared, which is approximately 3018 square kilometers.

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