Question

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

Explanation:

Step1: Find the central angle of the un - shaded sector

The total central angle of a circle is \(360^{\circ}\). The central angle of the shaded sector is \(60^{\circ}\). So, the central angle of the un - shaded sector \(\theta=360^{\circ}-60^{\circ} = 300^{\circ}\)

Step2: Use the sector area formula

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(r\) is the radius of the circle. Given \(r = 12\)
Substitute \(\theta = 300^{\circ}\) and \(r = 12\) into the formula:

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Answer:

\(120\pi\) units\(^{2}\)