The angle of a sector is π/4 radians, and the radius of the circle is 8 cm. What is the area of the sector?
8π cm^2
The area of a sector is given by \(\text{Area} = \frac{1}{2}r^2\theta\), where θ is in radians.
Substituting \(r=8\) and \(\theta = \frac{\pi}{4}\): \(\text{Area} = \frac{1}{2}(8)^2 \times \frac{\pi}{4} = \frac{1}{2} \times 64 \times \frac{\pi}{4}\).
Calculating, \(\frac{1}{2} \times 64 \times \frac{\pi}{4} = \frac{64\pi}{8} = 8\pi\).
Hence, the answer is 8π cm².
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