Question

For VHF signal broadcasting,_______$k{m}^2$of the maximum service area will be covered by an antenna tower of height $30m$, if the receiving antenna is placed on the ground. Let the radius of the earth be $6400km$. (Round off to the nearest integer) (Take $\pi =3.14$)

Answer 1

Step 1. Given data:

Height of antenna, $h=30m$

The radius of Earth, $R_e=6400km$

Step 2. Finding maximum service area:

The maximum line of sight distance is given by, $d=\sqrt{2h{R}_e}$

and the Service area is $A=\pi d^2$

$\Rightarrow A=3.14\times 2\times 30\times 6400\times {10}^3$

$\Rightarrow A=1205.7\times {10}^6{m}^2\approx 1206k{m}^2$

Hence, the correct answer is $1206$