Question

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

Explanation:

1. First, recall the formula for the area of a sector of a circle:

• The formula for the area of a sector of a circle with radius \(r\) and central - angle \(\theta\) (in degrees) is \(A=\frac{\theta}{360}\times\pi r^{2}\).
• Given that the radius \(r = 12\) and the central - angle of the shaded sector \(\theta=60^{\circ}\).
• The central - angle of the non - shaded sector is \(360 - 60=300^{\circ}\).

1. Then, calculate the area of the non - shaded sector:

• Substitute \(r = 12\) and \(\theta = 300\) into the area formula \(A=\frac{\theta}{360}\times\pi r^{2}\).
• \(A=\frac{300}{360}\times\pi\times(12)^{2}\).
• First, \((12)^{2}=144\). Then, \(\frac{300}{360}=\frac{5}{6}\).
• So, \(A=\frac{5}{6}\times\pi\times144\).
• \(\frac{5}{6}\times144 = 120\).
• The area of the non - shaded sector is \(120\pi\) square units.

Answer:

120π units²