# To warn ships for underwater rocks a lighthouse spreads a red coloured light over a sector of angle 80º to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use $$\pi \ = \ 3.14$$ )

Area of the sea over which the ships are warned

= Area of the sector
(having $$r \ = \ 16.5$$ km and $$\theta \ = \ 80°$$)

$$= \ \frac{ \theta }{360} \ × \ \pi r^2$$

$$= \ \frac{80}{360}\ × \ 3.14 \ × \ (16.5)^2$$

$$= \ \frac{68389.2}{360}$$

$$= \ 189.97$$ km2