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 $\pi = 3.14$)

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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 $189.97 \mathrm{~km}^{2}$.

Updated on 10-Oct-2022 13:24:02