In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the sector formed by the arc. Also, find the length of the arc.
Generated by claude-sonnet-4-6 · 2026-06-15 10:38 · grounding rag
Model Answer
Given: radius $r = 21$ cm, $\theta = 60°$, $\pi = \dfrac{22}{7}$
Area of the sector:
$$\text{Area} = \frac{\theta}{360} \times \pi r^2 = \frac{60}{360} \times \frac{22}{7} \times 21 \times 21$$
$$= \frac{1}{6} \times \frac{22}{7} \times 441 = \frac{1}{6} \times 1386 = \textbf{231 cm}^2$$
Length of the arc:
$$\text{Length} = \frac{\theta}{360} \times 2\pi r = \frac{60}{360} \times 2 \times \frac{22}{7} \times 21$$
$$= \frac{1}{6} \times 132 = \textbf{22 cm}$$
Source: Areas Related to Circles, Chapter 11 (Exercise 11.1, Q.5)
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Explanation
- Examiners expect you to state the formula first, then substitute values clearly — each step earns marks.
- Use $\pi = \dfrac{22}{7}$ as instructed; keep cancellations clean (21 cancels with 7).
- For a 3-mark question: 1 mark for correct formula/setup, 1 mark for area, 1 mark for arc length.
- Don't forget units (cm² for area, cm for length).