Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$4.71\text{ cm}^{2}$
We have: radius $r=3\text{ cm}$ central angle $\theta=60^{\circ}=\frac{\pi}{3}\text{ radians}$ The area of a sector is given by the formula $A=\frac{1}{2}r^{2}\theta$. Use this formula to obtain: $A=\frac{1}{2}\times (3\text{ cm})^{2}\times \frac{\pi}{3}$ $A=\frac{3\pi}{2}\text{ cm}^{2}\approx4.71\text{ cm}^{2}$ Thus, the area of the sector rounded to two decimal places is $4.71\text{ cm}^{2}$.