Sector Area

A sector is a slice of the disc. Its angle θ is the fraction $\frac{\theta}{2\pi}$ of a full turn, so its area is that fraction of the whole disc, $\pi\cdot {r}^{2}$. The π cancels:

$$A = \frac{1}{2}\cdot {r}^{2}\cdot \theta$$

The sector is π/3 out of 2π: one sixth of the disc.

With radius 6 and $\frac{\pi}{3}$: $A = \frac{\frac{1}{2}\cdot {6}^{2}\cdot \pi}{3}$, which is $6\pi$. Check it as a fraction: π/3 is a sixth of a turn, and a sixth of 36π is 6π. As with arcs, θ is in radians.