# A TV tower has a height of $100\: m$. The area covered by the TV broadcast, if radius of the earth is $6400\: km$, will be:

$\begin {array} {1 1} (a)\;380 \times 10^7 m^2 & \quad (b)\;402 \times 10^7 m^2 \\ (c)\;595 \times 10^7 m^2 & \quad (d)\;440 \times 10^7 m^2 \end {array}$

## 1 Answer

Distance covered by the broadcast, $d = \sqrt{2hR}$ , where R is the radius of Earth
$= \sqrt{(2 \times 100 \times 6400 \times 10^3 )}$
$= 35777.087\: m$
So, area covered $= \pi d^2$
$= 3.14 \times 35777.087^2 m^2$
$= 401.9 \times 10^7 m^2 \sim 40^2 \times 10^7 m^2$
Ans : (b)

answered Feb 28, 2014
edited Oct 3, 2014

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