Question

1. find the area of the orange sector.

$s = \frac{5\pi}{2}$ in.
$a = 9\pi$ in$^2$
$c = 6\pi$ in

Explanation:

Step1: Find circle radius

From $C=6\pi$, use $C=2\pi r$.
$$r=\frac{C}{2\pi}=\frac{6\pi}{2\pi}=3\text{ in}$$

Step2: Find sector ratio

Use arc length $s=\frac{5\pi}{2}$ and $C=6\pi$.
$$\text{Ratio}=\frac{s}{C}=\frac{\frac{5\pi}{2}}{6\pi}=\frac{5}{12}$$

Step3: Calculate sector area

Multiply ratio by total area $A=9\pi$.
$$\text{Sector Area}=\frac{5}{12} \times 9\pi=\frac{45\pi}{12}=\frac{15\pi}{4}$$

Answer:

$\frac{15\pi}{4}$ square inches