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 π = 3.14)

Given,

Lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km.

So, for sector :

Radius (r) = 16.5 km

Angle (θ) = 80°

We know that,

Area of sector of angle θ and radius r = $\dfrac{θ}{360°} \times πr^2$

Substituting values we get :

$\text{Area of sea over which ships are warned} = \dfrac{80°}{360°} \times 3.14 \times (16.5)^2 \\[1em] = \dfrac{2}{9} \times 3.14 \times 272.25 \\[1em] = \dfrac{1709.73}{9} \\[1em] = 189.97 \text{ km}^2.$

Hence, area of the sea over which the ships are warned = 189.97 km².