A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:
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Question

A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

G1 Physics · Accepted Answer

For a transmitting antenna of height h, the maximum line-of-sight distance is d = √(2Rh) The covered surface area is approximately A = πd² = π(2Rh) = 2πRh Given: R = 6400 km h = 98 m = 0.098 km Therefore, A = 2π(6400)(0.098) ≈ 3942 km² Hence option D follows.