Question

The required height of a TV tower which can cover the population of $6.03$ lakh is $h$. If the average population density is $100$ per square $km$ and the radius of earth is $6400\, km$, then the value of $h$ will be ______$m$.

Answer 1

$ d =\sqrt{2 Rh } $
$ d =\sqrt{2 \times 6400 \times h \times 10^{-3}}( h$ in $m )$
Area $=\pi d ^2 $
$ =\left(\pi \times 2 \times 6400 \times h \times 10^{-3}\right) km ^2 $
$ 6.03 \times 100000=100 \times \pi \times 2 \times 6400 \times 10^{-3} h $
$ h =\frac{6.03 \times 10^5}{10 \times \pi \times 128} $
$ h =150 \,m$