Question

A T.V. transmission tower at a particular station has height $160\text{m}$, earth's radius is $6400\text{km}$. What is population covered, if population density is $1200{\text{/km}}^2$ ?

• A. $50\text{Lakh}$
• B. $60.2\text{Lakh}$
• C. $77.24\text{Lakh}$
• D. $100.5\text{Lakh}$

Answer 1

The correct option is C $77.24\text{Lakh}$

Population density $\left(d_P\right)=1200{\text{per km}}^2$
coverage range $\left(dm\right)=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$
Where,
$R$ = Radius of earth
$h_T$ = height of transmission tower
$h_R$ = height of receiver
$dm=\sqrt{2(6400\times {10}^3)\left(160\right)}+\sqrt{2(6400\times {10}^3)\left(0\right)}$
$dm=45.254\text{km}$
Population density $=1200\times \left(\pi \right(dm{)}^2)=1200\times \pi \times (45.254{)}^2=77.24\text{lakhs}$