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The area of a sector of a circle of radius 6 cm with central angle \(120^\circ\) is:

1. 12 π cm²
2. 18 π cm²
3. 24 π cm²
4. 30 π cm²

Correct answer: 12 π cm²

Solution

The area of the full circle is \(\pi r^2=36\pi\). A \(120^\circ\) sector is one-third of the circle, so its area is \(\frac{120}{360}\times36\pi=12\pi\,\text{cm}^2\).

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