The area of a sector of a circle with radius [tex]r[/tex] and central angle [tex]\theta[/tex] is
[tex]A=\dfrac{r^2}2\theta[/tex]
which comes from the proportion relation,
[tex]\dfrac{\text{area of circle}}{\text{one full revolution}}=\dfrac{\pi r^2}{2\pi}=\dfrac A\theta=\dfrac{\text{area of sector}}{\text{measure of central angle (radians)}}[/tex]
You have [tex]30^\circ=\dfrac\pi6\text{ rad}[/tex], so the area is
[tex]A=\dfrac{6^2}2\times\dfrac\pi6=3\pi[/tex]
