Answer:
[tex]\text{area of sector} = \frac{320\pi}{3} \text{ mi}^2[/tex]
Step-by-step explanation:
Let's use the formula for the area of the sector:
[tex]\text{area of sector} = (\frac{\theta}{360^\circ}) \pi r^2[/tex],
where r is radius and θ the angle in degrees.
Given information:
r = 16 mi
θ = 150°
Using the formula:
[tex]\text{area of sector} = (\frac{\theta}{360^\circ}) \pi r^2 =\\\\ = (\frac{150^\circ}{360^\circ}) \pi (16\text{ mi})^2 =\\\\ = (\frac{150 \cdot 16^2}{360}) \pi \text{ mi}^2 =\\\\ = (\frac{320}{3}) \pi \text{ mi}^2 =\\\\ = \frac{320\pi}{3} \text{ mi}^2[/tex]
