A circle has radius $15\text{cm}$. Find the length of the arc subtended by a central angle of $120^{\circ }$, correct to two decimal places.

Step-by-step solution

1. Arc length formula: $l=\frac{\theta }{360^{\circ }}\times 2\pi r$.
2. Substitute $\theta =120^{\circ }$ and $r=15\text{cm}$: $l=\frac{120}{360}\times 2\pi \times 15$.
3. Simplify $\frac{120}{360}=\frac{1}{3}$ and $2\times 15=30$, so $l=\frac{1}{3}\times 30\pi =10\pi$.
4. Evaluate $10\pi \approx 31.4159$, round to two decimal places: $31.42\text{cm}$.

Concept tested: Length of an arc

Published 21 August 2026 · How this solution was prepared and checked

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