Multiple choice

A TV tower has a height of $100$m. The area covered by the TV broadcast, if radius of the earth is $6400$ km, will be?

  1. $380\times 10^7m^2$
  2. $402\times 10^7m^2$
  3. $595\times 10^7m^2$
  4. $440\times 10^7m^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area covered by a TV tower of height h is A = 2 * pi * R * h. Given h = 100 m = 0.1 km and R = 6400 km, A = 2 * 3.14 * 6400 * 0.1 = 4019.2 sq km. Converting to square meters: 4019.2 * (1000 m)^2 = 4019.2 * 10^6 m^2 = 401.92 * 10^7 m^2, which is approximately 402 * 10^7 m^2.

AI explanation

The area covered by a TV broadcast is calculated using the formula Area = 2 * pi * R * h, where R is the radius of the Earth and h is the height of the tower. Using the provided values in meters, Area = 2 * pi * 6400000 * 100. This gives 1280000000 * pi square meters. Taking pi as approximately 3.1416, the result is roughly 4021238520 square meters, which equals 402 x 10^7 m^2.

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