TV transmission tower at Kota has a height of 80 m. Radius of earth is 6400 km
(i) What is its coverage range
(ii) How much population is covered by transmission if the average population density around the tower is `2000 km^(-2)` ?

Explanation

Note : `h=80 m lt lt ltR=6400 km` Here `BC ~~ AC(because hlt lt ltR)`
`BC=sqrt((R+h)^(2)-R^(2))`
`BC=sqrt(2hR+h^(2))~~sqrt(2hR)`
Coverage range `= AC~~ BC=sqrt(2hR)`
(i) Coverage range `= sqrt(2xx80 xx6400xx10^(3))=32000m=32 km`
(ii) Coverage area `= pi(AC)^(2)=pi(32)^(2)km^(2)`
Population covered `= 2000 xx pi xx (32)^(2) = 6430720`