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.

Explanation

Given, sector angle `theta = 9=80^(@)`
and distance or radius r = 16.5 km
Area of sector `= (theta pi r^(2))/(360^(@)) = (80^(@) xx 3.14 xx (16.5)^(2))/(360^(@))`
`= (2 xx 3.14 xx 272.25)/(9) = (1709.73)/(9) = 189.97 km^(2)`
Which is the required area of the sea over which the ships are warned