Question

what is the area of the sector that is not shaded?

\\(12\pi\text{ units}^2\\)
\\(24\pi\text{ units}^2\\)
\\(120\pi\text{ units}^2\\)
\\(144\pi\text{ units}^2\\)

Explanation:

Calculate the central angle of the unshaded sector

$$ \theta_{\text{unshaded}} = 360^\circ - 60^\circ = 300^\circ $$

Calculate the total area of the circle

$$ A_{\text{total}} = \pi \cdot r^2 = \pi \cdot 12^2 = 144\pi $$

Calculate the area of the unshaded sector

$$ A_{\text{unshaded}} = \frac{300^\circ}{360^\circ} \cdot 144\pi = \frac{5}{6} \cdot 144\pi = 120\pi $$

Answer:

• (A) \(12\pi\text{ units}^2\)
• (B) \(24\pi\text{ units}^2\)
• (C) \(120\pi\text{ units}^2\) (Correct answer)
• (D) \(144\pi\text{ units}^2\)