Find the area of a sector of a circle with radius $6\text{ cm}$ if angle of the sector is $60^\circ$. (Take $\pi = 22/7$)
Step-by-Step Solution
Key Concept: $\text{Area} = \dfrac{\theta}{360^\circ} \times \pi r^2 = \dfrac{60}{360} \times \dfrac{22}{7} \times 36 = \dfrac{1}{6} \times \dfrac{22}{7} \times 36 = \dfrac{132}{7}\text{ cm}^2 = 18.86\text{ cm}^2$.
$\text{Area} = \dfrac{60}{360} \times \dfrac{22}{7} \times 6^2 = \dfrac{1}{6} \times \dfrac{22}{7} \times 36$. [1.0 Mark]
$= \dfrac{132}{7}\text{ cm}^2 = 18.86\text{ cm}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Applying sector area formula: 1.0 Mark
Evaluating area $= 132/7\text{ cm}^2$: 1.0 Mark
Correct Answer: