Question

A TV transmitting antenna is 80 m tall. If the receiving antenna is on the ground the service area is :

• A. 12 sq km
• B. 3215 sq km
• C. 144sq km
• D. 32 sq km

Answer 1

Answer: (B)

3215 sq km

The distance of recieving signal is given as:

$d_{max}=\sqrt{2R{H}_T}+\sqrt{2R{H}_R}{H}_T=80m{H}_R=0m{d}_{max}=\sqrt{\frac{2\times 6400\times 80}{1000}}=32km$

Thus, the area of service is given by:

$A=\pi {d_{max}}^2=\pi \times {32}^2=3125{km}^2$

Since the receiving area is circular in shape.