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# 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:**

We use the area of a sector of a circle to solve the given question.

The lighthouse spreads red coloured light over a sector of a circle with a radius 16.5 km and an angle of degree measure 80°

Area of the sea over which the ships are warned = Area of the sector of the circle with radius 16.5 km with an angle of degree measure 80°

= θ/360° × πr^{2}

= 80°/360° × πr^{2}

= 2/9πr^{2}

= 2/9 × 3.14 × 16.5 km × 16.5 km

= 189.97 km^{2}

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 12

**Video Solution:**

## 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)

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 12

**Summary:**

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. The area of the sea over which the ships are warned is 189.97 km^{2}.

**☛ Related Questions:**

- Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
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- The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
- A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use π = 3.14)

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