If the area covered by an FM radio station is | vedclass

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(B) The area $A$ covered by an antenna of height $h$ is given by the formula $A = \pi d^2$,where $d$ is the range of the antenna.Since $d = \sqrt{2Rh}

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$2$

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(B) The area $A$ covered by an antenna of height $h$ is given by the formula $A = \pi d^2$,where $d$ is the range of the antenna.Since $d = \sqrt{2Rh}$ (where $R$ is the radius of the Earth),the area is $A = \pi (2Rh) = 2\pi Rh$.This shows that the area $A$ is directly proportional to the height $h$ of the antenna $(A \propto h)$.If the area is to be doubled $(A' = 2A)$,then the new height $h'$ must satisfy $h' = 2h$.Therefore,the height of the antenna must be increased by a factor of $2$.

If the area covered by an $FM$ radio station is to be doubled,by what factor must the height of the antenna be increased?

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