Question

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 sector making angle $\theta$
$=\left(\frac{\theta }{{360}^{\circ }}\right)\times \pi r^2$
Area of the sea over which the ships are warned
= Area of the sector
$=\left(\frac{{80}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}k{m}^2$
$=\frac{2}{9}\times 3.14\times (16.5{)}^{2}k{m}^2=189.97k{m}^2$