A T.V. transmitting antenna is 80 m tall.  If receiving antenna is on the ground the service area is _____ sq.km.

$$\begin{gathered} The dis\tan ce of recieving signal is given as: \\ {\mathrm{d}}_{max}=\sqrt{2{\mathrm{RH}}_{\mathrm{T}}}+\sqrt{2{\mathrm{RH}}_{\mathrm{R}}} \\ {\mathrm{H}}_{\mathrm{T}}=80\mathrm{m} \\ {\mathrm{H}}_{\mathrm{R}}=0\mathrm{m} \\ {\mathrm{d}}_{max}=\sqrt{\frac{2\times 6400\times 80}{1000}}=32\mathrm{km} \\ \mathrm{Thus}, \mathrm{the} \mathrm{area} \mathrm{of} \mathrm{service} \mathrm{is} \mathrm{given} \mathrm{by}: \end{gathered}$$

$$\begin{gathered} \mathrm{A}=\pi {{\mathrm{d}}_{max}}^2=\pi \times {32}^2=3125{\mathrm{km}}^2 \\ Since the receiving area is circular in shape. \end{gathered}$$