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 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 = ` 80^@/360^@ xx pi r^2`

`= 2/9xx 3.14xx16.5xx16.5`

= 189.97 km²