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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 are warned. (Use π=3.14)

Solution:

When a lighthouse spreads a red-colored light underwater, it forms a sector of angle 80° and radius = 16.5 km
∴ Area of sector = θ/360 × π × r²
∴ Area of sector = 80/360 × 3.14 × 16.5 × 16.5 = 189.97 km²