MP Board · Class 10 · Mathematics · Areas Related to CirclesThe area of a sector of angle $60^\circ$ of a circle with radius 6 cm is:
Step-by-Step Solution
Area of sector = $\frac{\theta}{360^\circ} \times \pi r^2 = \frac{60^\circ}{360^\circ} \times \frac{22}{7} \times 6 \times 6 = \frac{1}{6} \times \frac{22}{7} \times 36 = \frac{22 \times 6}{7} = \frac{132}{7}\text{ cm}^2$.
Detailed Options Breakdown
Option : \frac{132}{7}\text{ cm}^2 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: \frac{66}{7}\text{ cm}^2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Areas Related to Circles.
Option 2: 132\text{ cm}^2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Areas Related to Circles.
Option 3: \frac{22}{7}\text{ cm}^2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Areas Related to Circles.
💡 Study Guide: This question tests core syllabus concepts from Areas Related to Circles. For formulas, key summaries, and mock exam reference guides, read the full Areas Related to Circles Revision Notes.