Question

In order to cover a circular region of radius 128 km, by a TV transmitter, What must be the height of the transmitting antenna ? 

(A) 79 m 

(B) 1050 m 

(C) 1280 m 

(D) 1560 m

Answer 1

The correct option is  (C) 1280 m.

Explanation:

Area of circular region = πR² = π × (128)² = 51.47 × 10³ km

We know area of transmission region = π(d²)  = π(√2hR)² = 2πRh

 ∴ Height of antenna = h = (area / 2πR)

= [(51.47 × 10³) / (2π × 6400)]

= 1.2799km

= 1280m