Question

to warn ships for underwater rocks, a light house spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. find the area of the sea which are spread with red color.

Answer 1

here you go. hope it helps

Answer 2

Answer:

The area of the sea spread with red color is 190 km²

Step-by-step explanation:

We are given that,

Angle made by the light, θ = 80°

Distance of the spread of light, r =16.5 kilometers

It is required to find the area of the sea spread with red color.

That is, we are required to find the sector area of the red color.

As, we know,

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

i.e. Area of the sector = $\frac{80}{360}\pi (16.5)^{2}$

i.e. Area of the sector = $0.222\times \pi \times 272.25$

i.e. Area of the sector = $0.222\times 3.14 \times 272.25$

i.e. Area of the sector = 189.8 km² ≈ 190 km²

Thus, the area of the sea spread with red color is 190 km²