Question

Question 12
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle ${80}^{\circ }$ to a distance of 16.5 km. Find the area of the sea over which the ships are warned.
$(Use\pi =3.14)$

Answer 1

Distance over which light spread i.e. radius, r = 16.5 km
Angle made by the sector $={80}^{\circ }$
Area of the sea over which the ships are warned
= Area of the sector.
= $\left(\frac{{80}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}k{m}^2=\frac{2}{9}\times 3.14\times \left(16.5\right)2k{m}^2=189.97k{m}^2$