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Areas Related to Circles
NCERT Exemplar
CBSE
Grade 10
Question:
Find the area of a sector of a circle with radius $4\text{ cm}$ and of angle $30^\circ$. Also, find the area of the corresponding major sector. (Use $\pi = 3.14$)
Step-by-Step Solution
Key Concept: Minor sector area $= \dfrac{30^\circ}{360^\circ} \pi r^2$. Major sector area $= \pi r^2 - \text{Minor sector area}$.
Minor sector area $= \dfrac{30}{360} \times 3.14 \times 4 \times 4 = \dfrac{1}{12} \times 3.14 \times 16 = \dfrac{50.24}{12} = 4.19\text{ cm}^2$. [1.0 Mark] Total area $= 3.14 \times 16 = 50.24\text{ cm}^2$. Major sector area $= 50.24 - 4.19 = 46.05\text{ cm}^2$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Calculating minor sector area $= 4.19\text{ cm}^2$: 1.0 Mark Calculating major sector area $= 46.05\text{ cm}^2$: 1.0 Mark
Correct Answer:
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