Question

A TV tower has a height of $100\, m$. How much population (in lakhs) is covered by TV transmission if the average population density around the tower is $1000 / km ^{2}$ ? (Radius of the Earth $=6.37 \times 10^{3} km$ ).

Answer 1

We are given that $h_{T}=100\, m =10^{-1} km$,
population density $=1000 / km ^{2}$
$d_{T}$ (radio horizon of the transmitting tower) $=\sqrt{2 R h_{T}}$
Area covered, $A=\pi d_{T}^{2}=2 \pi R h_{T}$
Population covered
$=2 \times 3.14\left(6.37 \times 10^{3} km \right)\left(10^{-1} km \right)\left(1000 / km ^{2}\right)$
$=40 \times 10^{5}=40 $ lakhs