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)

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Answer 1

$\huge \underline \mathbb {SOLUTION:-}$

Let O bet the position of Lighthouse.

• Figure provided in the above attachment.

Here the radius will be the distance over which light spreads.

Given:

• Radius (r) = 16.5 km
• Sector angle (θ) = 80°

Now, the total area of the sea over which the ships are warned = Area made by the sector

Or, Area of sector = (θ/360°) × π r²

= (80°/360°) × π r² km²

= 189.97 km²

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Answer 2

❥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.

❥ANSWER

Let O bet the position of Lighthouse.

Here the radius will be the distance over which light spreads.

Given, radius (r) = 16.5 km

Sector angle (θ) = 80°

Now, the total area of the sea over which the ships are warned = Area made by the sector

Or, Area of sector = (θ/360°)×πr2

= (80°/360°)×πr2 km2

= 189.97 km2