Question

circle m has a radius of 6 inches. what is the area of the shaded sector? write an exact, simplified answer. square inches

Explanation:

Step1: Recall area - of - a - sector formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central angle of the sector and $r$ is the radius of the circle.

Step2: Substitute the given values

We are given that $r = 6$ inches and $\theta=80^{\circ}$. Substitute these values into the formula: $A=\frac{80^{\circ}}{360^{\circ}}\times\pi\times(6)^{2}$.

Step3: Simplify the expression

First, simplify $\frac{80}{360}=\frac{2}{9}$. Then, $(6)^{2}=36$. So $A=\frac{2}{9}\times\pi\times36$. Multiply $\frac{2}{9}\times36 = 8$. So $A = 8\pi$.

Answer:

$8\pi$