A TV tower has a height of $5 \mathrm{~m}$ in a region of population density $\frac{1000}{\pi}$ per square kilometre. Number of people that can receive the transmission is nearly, (in thousands)

Given, height of a TV tower, $h=5 \mathrm{~m}$ population density, $n=\frac{1000}{\pi}$ Now, the maximum range of this transmission depends upon the height of transmitting antenna and is given by $d=\sqrt{2 h R_e}$. where, $h=$ height of tower and $R_e=$ Radius of earth $(R>>h)$ So, the number of people received the transmission, Population covered, $\left(P_c\right)=$ population density $(n) \times$ area of transmission range $(\mathrm{A})$ Population covered, $\left(P_c\right)=n \times A$ $$ P_c=\frac{1000}{\pi} \times \pi d^2 $$ Area of transmission range, or $$ \begin{gathered} A=\pi d^2 \text { or } P_c=1000 \times 2 h R_e \quad\left[\because d^2=2 h R_e\right] \\ P_c=1000 \times 2 \times 5 \times 10^{-3} \times 6400 \\ P_c=64000 \end{gathered} $$ So, the number of people received the transmission is 64000 .