If a transmitting antenna of height $105 \mathrm{~m}$ is placed on a hill, then its coverage area is

If a transmitting antenna of height $105 \mathrm{~m}$ is placed on a hill, then its coverage area is
  1. $4224 \mathrm{~km}^2$
  2. $3264 \mathrm{~km}^2$
  3. $6400 \mathrm{~km}^2$
  4. $4864 \mathrm{~km}^2$

Solution

$\begin{aligned} & \text { Coverage area } \mathrm{A}=\pi \mathrm{d}^2 \text { and } \mathrm{d}=\sqrt{2 R h} \\ & =\pi(\sqrt{2 R h})^2=\pi \times 2 R h \\ & \text { Here } h=105 \mathrm{~m}, R=6.4 \times 10^6 \mathrm{~m} \\ & \therefore \quad A=3.14 \times 2 \times 6.4 \times 10^6 \times 105 \mathrm{~m}^2 \\ & =314 \times 2 \times 64 \times 10^6 \times 105 \times 10^3 \mathrm{~m}^2 \\ & =4220.6 \mathrm{~km}^2=4224 \mathrm{~km}^2\end{aligned}$

Asked in: AP EAMCET 2016

Practice more Communication System questions on Aicharya