A sector of a circle having a radius of 10 cm and has a central angle of \(\frac{3\pi}{4}\) radians. What is the area of the sector?
\(37.5\,\pi\ \text{cm}^2\)
When the central angle is measured in radians, the area of a sector is \(\frac{1}{2} r^2 \theta\).
Here \(r = 10\) cm and \(\theta = \frac{3\pi}{4}\) radians.
So the area is \(\frac{1}{2} \times 10^2 \times \frac{3\pi}{4} = \frac{1}{2} \times 100 \times \frac{3\pi}{4}\).
This equals \(50 \times \frac{3\pi}{4} = \frac{150\pi}{4} = 37.5\,\pi\) cm².
Hence, the area of the sector is \(37.5\,\pi\ \text{cm}^2\).
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