To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of $16.5 \mathrm{~km}$. Find the area of the sea over which the ships are warned.
(Use $\pi=3.14$ )
Here, Radius (r) = 16.5 km and
Sector angle $(\theta)=80^{\circ}$
$\therefore$ Area of the sea surface over which the ships are warned
$=\frac{\theta}{\mathbf{3 6 0}^{\circ}} \times \pi^{2}=\frac{\mathbf{8 0}^{\circ}}{\mathbf{3 6 0}^{\circ}} \times \frac{\mathbf{3 1 4}}{\mathbf{1 0 0}} \times \frac{\mathbf{1 6 5}}{\mathbf{1 0}} \times \frac{\mathbf{1 6 5}}{\mathbf{1 0}} \mathrm{km}^{2}$
$=\frac{157 \times 11 \times 11}{100} \mathrm{~km}^{2}=\frac{18997}{100} \mathrm{~km}^{2}$
$=189.97 \mathrm{~km}^{2}$
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