Find the area of the sector of a circle of radius 42 cm and of central angle 30°. Also, find the area of the corresponding major sector. [Use $\pi = \frac{22}{7}$]
Generated by claude-sonnet-4-6 · 2026-06-15 10:38 · grounding rag
Model Answer
Given: Radius $r = 42$ cm, $\theta = 30°$, $\pi = \dfrac{22}{7}$
Area of minor sector:
$$= \frac{\theta}{360} \times \pi r^2 = \frac{30}{360} \times \frac{22}{7} \times 42 \times 42$$
$$= \frac{1}{12} \times \frac{22}{7} \times 1764 = \frac{1}{12} \times 5544 = 462 \text{ cm}^2$$
Area of major sector:
$$= \pi r^2 - \text{Area of minor sector}$$
$$= \frac{22}{7} \times 42 \times 42 - 462 = 5544 - 462 = 5082 \text{ cm}^2$$
Source: Areas of Sector and Segment of a Circle, Chapter 11
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Explanation
- Use the formula: Area of sector $= \dfrac{\theta}{360} \times \pi r^2$.
- Area of major sector = Total area of circle − Area of minor sector. Alternatively, use angle $(360° - 30°) = 330°$ directly in the formula — both give the same answer.
- Show all calculation steps clearly; examiners award marks for correct substitution, simplification, and final answer.