Arc length and area of a sector.

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Presentation transcript:

Arc length and area of a sector

Arc Length An arc of a circle is a portion of the circumference formed by a central angle. It’s the length of the pie crust! θ

Arc Length The arc length s of a circle radius r, subtended by a central angle of θ radians, is given by: s = rθ The angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!

“Subtended?” That just means “formed by.” Example 1: Arc Length Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian. “Subtended?” That just means “formed by.”

Area of a Sector A sector of a circle is a portion of the circle formed by a central angle. It’s the area of a slice of pie! θ

Area of a Sector The area of a sector A of a circle radius r, subtended by a central angle of θ radians, is given by: A = ½r2θ Again, the angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!

Example 2: Area of a Sector Find the area of the sector of a circle of radius 5 feet subtended by an angle of 60°. Round the answer to two decimal places. “Subtended?” That just means “formed by.”

Put it all together! Arc Length Area of a Sector s = rθ A = ½r2θ Length of pie crust Area of a slice