Circles and Sectors

Circles
What are the length of AC, the approximate area of circle A rounded to the nearest hundredth, and the exact area of circle A?
What are the the approximate radius of circle c rounded to the nearest hundredth, the exact diameter of circle c, and the exact circumference of circle c?
Sectors
What are the exact areas of sectors BAC and CAB?
If sector c has an area of 4[math]\pi[/math], what are the radius and diameter of the circle, and the exact circumference?
Complex shapes
What is the approximate area of the green outer ring rounded to the nearest tenth?
What is the exact area of the circle that isn't filled in by the triangle(s)?
Real world
Your doing a study for a marketing team. About 210,000 people live in a circular region with a 12-mile radius. Find the population density in people per square mile.
While reading/listening to a news story you get this information: "A circular region with a 4-mile radius has a population density of about 6366 people per square mile." [br]Find the number of people who live in the region.
While helping run a fund raising event you are told that about 79,000 people live in the roughly circular region they need you to help cover. It has a population density of about 513 people per square mile. Find the radius of the region. If the team you're working with has 20 members, including you, and each one takes an equal sector of the area, how many square miles are you covering? Round your answers to the nearest whole number.
If you have a lawn sprinkler that covers a 145[math]^\circ[/math] arc, how much of your lawn does it cover in square feet when the pressure gets the water up to 15 feet from the sprinkler? What happens if you reduce the pressure to reach 12 feet instead? Round your answers to the nearest whole number.
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Information: Circles and Sectors