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 $16.5km$. Find the area of the sea over which the ships are warned. (Use $\pi =3.14$)

Answer 1

When a lighthouse spreads a red-colored light underwater, it forms a sector of angle ${80}^o$ and radius $=16.5km$

$\therefore$ Area of sector $=\frac{\theta }{360}\times \pi \times r^2$

$\therefore$ Area of sector $=\frac{80}{360}\times 3.14\times 16.5\times 16.5$
$=189.97k{m}^2$