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A sector of a circle has a central angle of $120^{\circ}$ and a radius of 4 inches. Find the area of the sector.

$\cfrac{16 \pi}{3} \text{ in}^2$

$\cfrac{4 \pi}{3} \text{ in}^2$

$\cfrac{32 \pi}{3} \text{ in}^2$

$16 \pi \text{ in}^2$

$\cfrac{8 \pi}{3} \text{ in}^2$