Answer
$\frac{9\pi}{10}\approx2.83$ m$^{2}$
Work Step by Step
If $\theta$ (in radians) is a central angle in a circle with radius $r$, then the area of the sector formed by angle $\theta$ can be calculated as $A=\frac{1}{2}r^{2}\theta$.
We are given that $\theta=\frac{\pi}{5}$ and $r=3$ m.
Therefore, $A=\frac{1}{2}(3^{2})(\frac{\pi}{5})=\frac{1}{2}(9)(\frac{\pi}{5})=\frac{1\times9\times\pi}{2\times5}=\frac{9\pi}{10}\approx2.83$ m$^{2}$.
