Question

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)

Answer 1

It can be observed from the figure that the lighthouse spreads light across a sector of 80° in a circle of 16.5 km radius.

Area of sector OACB = \(\frac{80°}{360°} \times \pi r ^2\)

                                 = \(\frac{2}{9} \times 3.14 \times 16.5 \times 16.5\)

                                 = \(189.97\,km^2\)