what is the area of the sector that is not shaded? 12π units² 24π units² 120π units² 144π units²
what is the area of the sector that is not shaded? 12π units² 24π units² 120π units² 144π units²
Answer
Explanation:
Step1: Find the central - angle of non - shaded sector
The total angle in a circle is $360^{\circ}$. The shaded sector has a central angle of $60^{\circ}$, so the central angle of the non - shaded sector $\theta=360^{\circ}-60^{\circ}=300^{\circ}$.
Step2: Recall the formula for the area of a sector
The formula for the area of a sector of a circle with radius $r$ and central angle $\theta$ (in degrees) is $A = \frac{\theta}{360}\times\pi r^{2}$. Here, $r = 12$.
Step3: Calculate the area of the non - shaded sector
Substitute $\theta = 300$ and $r = 12$ into the formula: $A=\frac{300}{360}\times\pi\times12^{2}=\frac{5}{6}\times\pi\times144 = 120\pi$ square units.
Answer:
$120\pi$ units$^{2}$