To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use $\pi = 3.14$)
Given:
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^o$ to a distance of 16.5 km.
To do:
We have to find the area of the sea over which the ships are warned.
Solution:
Angle of the sector $= 80^o$
Distance covered $= 16.5\ km$
This implies,
Radius of the sector formed $= 16.5\ km$
Therefore,
Area of the sea over which ships are warned $=$ Area of the sector
$=\frac{\pi r^{2} \theta}{360^{\circ}}$
$=\frac{3.14 \times 16.5 \times 16.5 \times 80^{\circ}}{360^{\circ}}$
$=189.97 \mathrm{~km}^{2}$
The area of the sea over which the ships are warned is $189.97 \mathrm{~km}^{2}$.
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