Question 6 of 7intermediate🔧 ApplyNumerical3 marks

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)

Correct Answer

189.97 km²

Exercise: EXERCISE 11.1 | Q: 12 | (Page Page 6)
For More Understanding

Explanation

The question requires calculating the area of a sector. The provided context explicitly states the formula for the area of a sector as (θ/360) × πr², derived using the unitary method. By identifying the radius (r) as 16.5 km and the angle (θ) as 80° from the problem statement, and substituting the given value of π = 3.14, we can compute the area. The calculation follows the standard procedure shown in the textbook examples for finding sector areas.

Solution Steps

  1. Given: Radius (rr) = 16.5 km and sector angle (θ\theta) = 80°.

  2. Formula: Area of the sector = θ360×πr2\frac{\theta}{360} \times \pi r^2.

  3. Substitution: Area = 80360×3.14×(16.5)2\frac{80}{360} \times 3.14 \times (16.5)^2.

  4. Calculation: Area = 29×3.14×272.25\frac{2}{9} \times 3.14 \times 272.25.

  5. Solving: Area = 60.5×3.14=189.9760.5 \times 3.14 = 189.97 km².

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