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Areas Related to Circles
NCERT Exemplar
CBSE
Grade 10

Question:

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^\circ$ to a distance of $16.5\text{ km}$. Find the area of the sea over which the ships are warned. (Use $\pi = 3.14$)

Step-by-Step Solution

Key Concept: Area $= \dfrac{80}{360} \pi (16.5)^2$.
Area $= \dfrac{80}{360} \times 3.14 \times 16.5 \times 16.5 = \dfrac{2}{9} \times 3.14 \times 272.25$. [1.5 Marks]
$= \dfrac{2}{9} \times 854.865 = \dfrac{1709.73}{9} = 189.97\text{ km}^2$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Formula setup with $\theta = 80^\circ, r = 16.5\text{ km}$: 1.5 Marks
Evaluating area $= 189.97\text{ km}^2$: 1.5 Marks

Correct Answer:
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