Ex 11.1 Q12 - 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:-Given,
The light house spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km,
Therefore,
Radius = r = 16.5 km
Angle = 𝜃 = 80°
➙ We know that, Area of the sector of angle '𝜃' and radius 'r' is given by,
Area =
𝜃
/
360°
× πr² ∴ Area of sea over which ships are warned,
= Area of the sector of angle 80° and
radius 16.5 km
=
280°
/
360°
× 3.14 × (16.5)² =
2
/
9
× 3.14 × 16.5 × 16.5 =
1709.73
/
9
= 189.97 km²
Hence,
The area of the sea over which the ships are warned is 189.97 km².
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Try This..
✒ A wheel of radius 14 cm is rolling. How much area will the sector cover in 45°?
✒ Find the area of a sector of radius 7 cm and angle 60°.
✒ A sprinkler waters a circular area of radius 10 m. If it covers 90°, find the area watered.
❌ Common Mistakes
Using wrong angle unit:▸ Always make sure the angle is in degrees, not radians, unless specified.Incorrect radius usage:▸ Double-check if the distance given is diameter or radius.Forgetting to square the radius:▸ This is a common calculation error.Rounding too early:▸ Always calculate using full values, round off only in the final step.Wrong formula:▸ Don't mix it up with circumference or full circle area.
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Queries Solved:-
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Class 10 Areas Related To Circles
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