what is the area of the shaded sector of the circle? 9π units² 27π units² 81π units² 162π units²
what is the area of the shaded sector of the circle? 9π units² 27π units² 81π units² 162π units²
Answer
Explanation:
Step1: Recall area - of - circle formula
The area of a full - circle is given by $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, $r = 9$, so the area of the full - circle $A_{total}=\pi\times9^{2}=81\pi$.
Step2: Use sector - area formula
The area of a sector of a circle with central angle $\theta$ (in degrees) is $A_{sector}=\frac{\theta}{360}\times A_{total}$. Given $\theta = 120^{\circ}$, then $A_{sector}=\frac{120}{360}\times81\pi$.
Step3: Simplify the expression
$\frac{120}{360}\times81\pi=\frac{1}{3}\times81\pi = 27\pi$.
Answer:
$27\pi$ units$^{2}$