Question

Area of a sector of a radius 6 inches and 30 degrees

Answer 1

The area of a sector of a circle with radius $r$ and central angle $\theta$ is

$A=\dfrac{r^2}2\theta$

which comes from the proportion relation,

$\dfrac{\text{area of circle}}{\text{one full revolution}}=\dfrac{\pi r^2}{2\pi}=\dfrac A\theta=\dfrac{\text{area of sector}}{\text{measure of central angle (radians)}}$

You have $30^\circ=\dfrac\pi6\text{ rad}$, so the area is

$A=\dfrac{6^2}2\times\dfrac\pi6=3\pi$