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Find the area of a sector of a circle with radius 12 cm and central angle \(\pi/5\) radians.

1. 30.16 cm²
2. 45.24 cm²
3. 60.48 cm²
4. 75.6 cm²

Correct answer: 45.24 cm²

Solution

For a sector with angle in radians, area = \(\frac{1}{2}r^2\theta\). Substituting \(r=12\) and \(\theta=\pi/5\) gives \(\frac{1}{2}\times 144 \times \frac{\pi}{5} = 14.4\pi \approx 45.24\,\text{cm}^2\).

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