Question

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

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

Answer 1

The correct option is A

$60.288lakh$

Step 1. Data Given:

Height of the TV tower $h=150m$

Population density $\rho ={10}^{3}k{m}^{-2}$

$={10}^{-3}{m}^2$

The radius of the Earth $R=6.4\times {10}^{6}m$

Step 2. Find the population covered:

If $d$is the distance up to which the transmission can be received then,

$d=\sqrt{2hR}$

Then total area covered $=\pi d^2$

$=2\pi hR$

Now the population covered is given by

$={10}^{-3}\times 2\pi hR$

$={10}^{-3}\times 2\times 3.14\times 150\times 6.4\times {10}^6$

$=60.288lakh$

Hence option (A) is correct.