Question

the measure of central angle ycz is 80 degrees. what is the sum of the areas of the two shaded sectors? 18π units² 36π units² 45π units² 81π units²

Explanation:

Step1: Recall sector - area 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 measure and $r$ is the radius of the circle.

Step2: Identify the radius and central - angle measures

The radius of the circle $r = 9$, and the two shaded sectors have central - angle measures. Since the circle is symmetric, the two shaded sectors together have a central - angle measure of $\theta=80^{\circ}+80^{\circ}=160^{\circ}$.

Step3: Calculate the area of the two shaded sectors

Substitute $\theta = 160^{\circ}$ and $r = 9$ into the sector - area formula:
\[

$$\begin{align*} A&=\frac{160^{\circ}}{360^{\circ}}\times\pi\times9^{2}\\ &=\frac{4}{9}\times\pi\times81\\ & = 36\pi \end{align*}$$

\]

Answer:

$36\pi$ units$^{2}$