Find the area of a sector of a circle with radius $6\text{cm}$ and central angle $60^{\circ }$.

Step-by-step solution

1. Area of a sector: $\text{Area}=\frac{\theta }{360^{\circ }}\pi r^2$, where $\theta$ is in degrees.
2. Substitute $\theta =60^{\circ }$ and $r=6\text{cm}$: $\text{Area}=\frac{60}{360}\pi \times 6^2$.
3. Simplify the fraction $\frac{60}{360}=\frac{1}{6}$ and $6^2=36$: $\text{Area}=\frac{1}{6}\pi \times 36$.
4. Compute: $\text{Area}=6\pi {\text{cm}}^2$.

Concept tested: Area of sector

Published 22 August 2026 · How this solution was prepared and checked

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