Answer-
The area of the sector not shaded is [tex]120\pi[/tex]
Solution-
Here,
The angle of the sector = Θ = 60°
Radius of the circle = 12
Then area of the circle will be,
[tex]\text{Area}=\pi \times \text{Radius}^2[/tex]
Putting the values,
[tex]\text{Area}=\pi \times 12^2=144\pi[/tex]
We also know that, the area of sector is,
[tex]\text{Area of the sector}=\dfrac{\theta}{360^{\circ}}\times \text{Area of the circle}[/tex]
where, angle of the sector is measured in degrees.
Putting the values,
[tex]\text{Area of the sector}=\dfrac{60^{\circ}}{360^{\circ}}\times 144\pi\\\\=\dfrac{1}{6}\times 144\pi\\\\=24\pi[/tex]
Therefore, the area of the sector not shaded = 144π-24π = 120π
