Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm.
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer
Given: radius $r = 42$ cm, angle $\theta = 60°$, $\pi = \dfrac{22}{7}$
Length of arc $= \dfrac{\theta}{360} \times 2\pi r$
$$= \frac{60}{360} \times 2 \times \frac{22}{7} \times 42$$
$$= \frac{1}{6} \times 2 \times \frac{22}{7} \times 42 = \frac{1}{6} \times 264 = 44 \text{ cm}$$
Length of the arc = 44 cm
Source: Chapter 11, Section 11.1 (Areas of Sector and Segment of a Circle)
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Explanation
- The formula for arc length is $\dfrac{\theta}{360} \times 2\pi r$ — memorise this.
- Simplify step-by-step: cancel $\frac{60}{360} = \frac{1}{6}$, then $\frac{42}{7} = 6$, making arithmetic clean.
- Always substitute $\pi = \frac{22}{7}$ unless told otherwise.
- Write the final answer with units (cm).