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 ${10}^{3}k{m}^{-2}?$ Radius of the earth is $6.4\times {10}^6$m.

• A. $60.288$lakh
• B. $40.192$lakh
• C. $100$lakh
• D. $20.228$lakh

Answer 1

Answer: (A)

$60.288$lakh

$h=150m,R=6.4\times {10}^6$m
Average population density $={10}^{3}k{m}^{-2}$
$=\left({10}^3\right)({10}^3{)}^{-1}{m}^{-2}={10}^{-3}{m}^{-2}$
Distance upto which the transmission could be viewed
$d=\sqrt{2hR}$
Total area over which transmission could be viewer
$=\pi d^2=2\pi hR$
Population covered $={10}^{-3}\times 2\pi hR$
$={10}^{-3}\times 2\times 3.14\times 150\times 6.4\times {10}^6$
$=60.288$lakh.