Question

A TV tower has a height 150 m. What is the total population covered by the TV tower, if the population density around the TV tower is $10^3\, km^{-2}?$ Radius of the earth is $6.4\times10^{6}m$

• A. 60.288 lakh
• B. 40.192 lakh
• C. 100 lakh
• D. 20.22 lakh

Answer 1

Answer: (A)

60.288 lakh

Answer 2

$h =150\, m,R = 6.4 \times 10^{6}\, m$
Average population density $= 10^3\, km^{-2}$
\hspace25mm = (10^3) (10^3) m^{-2} = 10^{-3}\, m^{-2}
Distance upto which the transmission could be viewed
\hspace30mm d = \sqrt{2hR}
Total area over which transmission could be viewer
\hspace30mm = \pi d^2 = 2 \pi h R
Population covered $= 10^{-3} \times 2 \pi h R$
\hspace40mm = 10^{-3} \times 2 \times 3.14 \times 150 \times 6.4 \times 10^6
\hspace40mm = 60.288\, lakh