Question

A TV tower has a height of $75m$. The maximum distance and area up to which this TV transmission can be received is

(Radius of the Earth = $6400km$)

• A. $31km$, $3018{km}^2$
• B. $30km$, $3000{km}^2$
• C. $28km$, $2800{km}^2$
• D. $25km$, $2500{km}^2$

Answer 1

The correct option is A $31km$, $3018{km}^2$

Distance upto which the transmission could be viewed is:

$d=\sqrt{2hR}$

$d=\sqrt{2\times 0.075\times 6.4\times {10}^3}=31km$

Total area over which the transmission could be viewed is:

$A=2\pi hR$

$=2\times 3.14\times 0.075\times 6.4\times {10}^3=3018k{m}^2$