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A TV transmission tower of antenna is at...

A TV transmission tower of antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) at ground level (ii) at a height of 25 m ? Calculate the percentage increase in area covered in case (ii) relative to case (i). Radius of earth =6.4×106m

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The correct Answer is:
B, C, D
(i) When receiver is at ground level, then service area covered.
=`pid^2=pi(sqrt(2Rh))^(2)`
=`2piRh`
=`2xx pixx6.4xx 10^6xx20`
=`804 km^2`
(ii) When receiver is at height of 25 m,area covered.
=`pid_1^2 + pid_2^2`
=`pi(sqrt(2Rh_(T)))^(2)+ pi(sqrt(2Rh_(R)))^(2)`
=`2piR(h_T +h_R)`
=`2xx pixx6.4xx10^6xx45(m^2)`
`~~ 3608 km^(2)`
(iii) Percentage increase in area covered.
=`(A_2-A_1)/(A_1)xx 100`
=`(3608-804)/(804)xx100`
=`349 %`.
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