Question

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Answer 1

`\text{area of sector} = (320\pi)/(3) \text{ mi}^2`

Explanation:

Let's use the formula for the area of the sector:

`\text{area of sector} = ((\theta)/(360^\circ)) \pi r^2`,
where r is radius and θ the angle in degrees.

Given information:

r = 16 mi

θ = 150°

Using the formula:

`\text{area of sector} = ((\theta)/(360^\circ)) \pi r^2 =\\\\ = ((150^\circ)/(360^\circ)) \pi (16\text{ mi})^2 =\\\\ = ((150 \cdot 16^2)/(360)) \pi \text{ mi}^2 =\\\\ = ((320)/(3)) \pi \text{ mi}^2 =\\\\ = (320\pi)/(3) \text{ mi}^2`