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What should be the height of transmitting antenna if the T.V. telecast is to cover a radius of 128 km? `R_e = 6.4 xx 10^6`m. If the average population density around the tower is `1000//km^2`, how much population is covered?

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The correct Answer is:
1280m
Here, d = 128 km `= 128 xx 10^(3) m, R = 6.4 xx 10^6 m` , population density `= 1000//km^2`
Height of transmitting antenna ` h = d^2/(2R) = (128 xx 10^3)^2/(2 xx 6.4 xx 10^6) = 1280m.`
Total population covered `= pid^2 xx` population density `= 3.14 xx (128)^2 xx 1000 = 5.14 xx 10^7`.
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