Given a circle with a radius of $12$ units and a central angle of $120°$, what is the area of the sector that is not shaded if the shaded sector corresponds to the given central angle? Choose the closest value.

• A. $144$
• B. $24$
• C. $12$
• D. $120$

Answer: (A)

Verified step by step guidance

1. Identify the total area of the circle using the formula \(A = \pi r^{2}\), where \(r\) is the radius of the circle.
2. Calculate the area of the shaded sector using the formula for the area of a sector: \(A_{\text{sector}} = \frac{\theta}{360^{\circ}} \times \pi r^{2}\), where \(\theta\) is the central angle in degrees.
3. Substitute the given values: radius \(r = 12\) units and central angle \(\theta = 120^{\circ}\) into the sector area formula.
4. Calculate the area of the sector that is not shaded by subtracting the shaded sector area from the total area of the circle: \(A_{\text{not shaded}} = A_{\text{circle}} - A_{\text{sector}}\).
5. Compare the calculated area of the non-shaded sector with the given answer choices to select the closest value.