Area of a sector of central angle $60^\circ$ of a circle with radius $6\text{ cm}$ is:
(a) $\dfrac{132}{7}\text{ cm}^2$
(b) $\dfrac{132}{14}\text{ cm}^2$
(c) $\dfrac{66}{7}\text{ cm}^2$
(d) $36\pi\text{ cm}^2$
Step-by-Step Solution
Key Concept: Sector area $= \dfrac{60^\circ}{360^\circ} \pi (6)^2 = \dfrac{1}{6} \times \dfrac{22}{7} \times 36 = \dfrac{132}{7}\text{ cm}^2$.
Area $= \dfrac{1}{6} \times \dfrac{22}{7} \times 36 = \dfrac{132}{7}\text{ cm}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating sector area $= 132/7\text{ cm}^2$: 1.0 Mark
Correct Answer: $\dfrac{132}{7}\text{ cm}^2$