Question

The area of the region covered by the TV broadcast by a TV tower of 100 m height is (Radius of the earth = $ 6.4 \times 10^6 \, m $ )

• A. $ 12.8 \pi \times 10^8 \, km^2 $
• B. $ 1.28 \pi \times 10^3 \, km^2 $
• C. $ 0.644 \pi \times 10^3 \, km^2 $
• D. $ 1.28 \pi \times 10^3 \, km^2 $
• E. $ 2.56 \pi \times 10^3 \, km^2 $

Answer 1

Answer: (B)

Area of broadcast is
A = $ \pi d^2 = \pi \, ( 2hR ) $
Given, $ h = 100 mR = 6.4 \times 10^6 \, m $
$\Rightarrow A = \pi ( 2 \times 100 \times 6.4 \times 10^6 ) $
A = $ 1.28 \pi \times 10^3 \, km^2 $