Question

what is the area of the sector that is not shaded? 12π units² 24π units² 120π units² 144π units²

Explanation:

Step1: Find the area of the whole circle

The formula for the area of a circle is $A = \pi r^{2}$. Given $r = 12$, so $A=\pi\times12^{2}=144\pi$.

Step2: Find the central - angle of the non - shaded sector

The central - angle of the shaded sector is $60^{\circ}$, and the total central - angle of a circle is $360^{\circ}$. So the central - angle of the non - shaded sector is $360 - 60=300^{\circ}$.

Step3: Find the area of the non - shaded sector

The formula for the area of a sector is $A_{s}=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector. Substituting $\theta = 300$ and $r = 12$ into the formula, we get $A_{s}=\frac{300}{360}\times144\pi = 120\pi$.

Answer:

$120\pi$ units$^{2}$