For $VHF$ signal broadcasting, _____ ${km}^{2}$ of maximum service area will be covered by an antenna tower of height $30 m$ , if the receiving antenna is placed on the ground.

$($ Let radius of the earth be $6400 km)$
$($ Round off to the nearest integer $)$
$($ Take $π$ as $3.14)$

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Solution

We know that radius of the area covered,
$r = \sqrt{2 h R}$

Also, area,
$A = π r^{2}$
$\Rightarrow A = π (2 h R)$
$\Rightarrow A = 3.14 \times 2 \times 30 \times 6400 \times 10^{3}$
$\Rightarrow A \approx 1206 \times 10^{6} m^{2} \approx 1206 {km}^{2}$

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For VHF signal broadcasting, _____ km2 of maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed on the ground. (Let radius of the earth be 6400 km) (Round off to the nearest integer) (Take π as 3.14)

We know that radius of the area covered, r=√2hR Also, area, A=πr2 ⇒A=π(2hR) ⇒A=3.14×2×30×6400×103 ⇒A≈1206×106 m2≈1206 km2

For $VHF$ signal broadcasting, _____ ${km}^{2}$ of maximum service area will be covered by an antenna tower of height $30 m$ , if the receiving antenna is placed on the ground.

$($ Let radius of the earth be $6400 km)$
$($ Round off to the nearest integer $)$
$($ Take $π$ as $3.14)$

We know that radius of the area covered,
$r = \sqrt{2 h R}$

Also, area,
$A = π r^{2}$
$\Rightarrow A = π (2 h R)$
$\Rightarrow A = 3.14 \times 2 \times 30 \times 6400 \times 10^{3}$
$\Rightarrow A \approx 1206 \times 10^{6} m^{2} \approx 1206 {km}^{2}$