Answer:
The answer is "169.56 units".
Explanation:
Given:
[tex]\to r= 9 \\\\ \to \theta = 360^{\circ} - 120^{\circ} = 240^{\circ}[/tex]
[tex]= \frac{ 2 \pi }{360^{\circ}} \times 120\\\\= \frac{ 2 \times 3.14 }{360^{\circ}} \times 120\\\\= \frac{ 2 \times 3.14 }{360^{\circ}} \times 120\\\\=2.093333333333333333333[/tex]
Calculating the area of the sector:
[tex]=\pi \ r^2 - \pi r^2 \frac{\theta }{360}\\\\=\pi \ r^2(1 - \frac{120}{360})\\\\=\pi \ r^2(\frac{360-120}{360})\\\\=3.14 \times 9^2(\frac{240}{360})\\\\=3.14 \times 81 \times (\frac{2}{3})\\\\=6.28 \times 27 \\\\=169.56 \ \[/tex]
The area of the shaded sector is 84.78 units².
where
r = radius
∅ = centre angle
Therefore,
r = 9 units
∅ = 120°
area of the sector = 120 / 360 × 3.14 × 9²
area of the sector = 120 / 360 × 3.14 × 81
area of the sector = 30520.8 / 360
area of the sector = 84.78 units
Therefore, the area of the shaded sector is 84.78 units².
learn more on sector here:https://brainly.com/question/1582027
