what is the area of the shaded sector of the circle? 20π units² 40π units² 180π units² 400π units²
what is the area of the shaded sector of the circle? 20π units² 40π units² 180π units² 400π units²
Answer
Explanation:
Step1: Recall sector - area formula
The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle.
Step2: Identify the values of $\theta$ and $r$
From the problem, $\theta = 162^{\circ}$ and $r = 20$.
Step3: Substitute the values into the formula
$A=\frac{162}{360}\times\pi\times(20)^{2}$. First, calculate $\frac{162}{360}=\frac{9}{20}$. Then, $(20)^{2}=400$. So, $A=\frac{9}{20}\times\pi\times400$. $A = 180\pi$ square units.
Answer:
$180\pi$ units$^{2}$