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