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(B) The area $A$ covered by an $FM$ antenna of height $h_T$ is given by the formula $A = \pi d^2$,where $d$ is the line-of-sight distance given by $d

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(B) The area $A$ covered by an $FM$ antenna of height $h_T$ is given by the formula $A = \pi d^2$,where $d$ is the line-of-sight distance given by $d = \sqrt{2Rh_T}$.Substituting $d$ into the area formula,we get $A = \pi (2Rh_T) = 2\pi Rh_T$.Since $2$,$\pi$,and $R$ (radius of the Earth) are constants,the area $A$ is directly proportional to the height of the antenna $h_T$,i.e.,$A \propto h_T$.If the area $A$ is to be tripled $(A' = 3A)$,then the new height $h_T'$ must satisfy $A' \propto h_T'$,which implies $3A \propto h_T'$.Therefore,$h_T' = 3h_T$.Thus,the height of the antenna must be increased to $3$ times its original height.

If the area covered by an $FM$ radio station is to be tripled,the height of the antenna must be .......

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