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## 11.4 Circumference and Arc Length

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**11.4 Circumference and Arc Length**2/17/2011**Objectives**• Find the circumference of a circle and the length of a circular arc. • Use circumference and arc length to solve real-life problems.**Finding circumference and arc length**• The circumference of a circle is the distance around the circle. • For all circles, the ratio of the circumference to the diameter is the same. This ratio is known as or pi.**Theorem 11.6: Circumference of a Circle**• The circumference C of a circle is C = d or C = 2r, where d is the diameter of the circle and r is the radius of the circle.**Ex. 1: Using circumference**• Find (Round decimal answers to two decimal places) • (a) the circumference of a circle with radius 6 centimeters and • (b) the radius of a circle with circumference 31 meters.**What’s the difference??**• Find the exact radius of a circle with circumference 54 feet. • Find the radius of a circle with circumference 54 feet.**Extra Examples Write below previous box**• Find the exact circumference of a circle with diameter of 15. • Find the exact radius of a circle with circumference of 25.**And . . .**• An arc length is a portion of the circumference of a circle. • You can use the measure of an arc (in degrees) to find its length (in linear units).**Finding the measure of an Arc Length**• In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360°. m • 2r Arc length of = 360°**More . . .**½ • 2r • The length of a semicircle is half the circumference, and the length of a 90° arc is one quarter of the circumference. d ¼ • 2r**Ex. 2: Finding Arc Lengths**• Find the length of each arc. a. c. 50° 100°**Ex. 2: Finding Arc Lengths**• Find the length of each arc. b. 50°**Ex. 2: Finding Arc Lengths**• Find the length of each arc. c. 100°**Find the length of each arc.**• 2(5) a. Arc length of = 50° 360° Ex. 2: Finding Arc Lengths # of ° a. • 2r a. Arc length of = 360° 50° 4.36 centimeters**Ex. 2: Finding Arc Lengths**• Find the length of each arc. # of ° b. • 2r b. Arc length of = 360° 50° 50° • 2(7) b. Arc length of = 360° 6.11 centimeters**Find the length of each arc.**Ex. 2: Finding Arc Lengths # of ° c. • 2r c. Arc length of = 360° 100° 100° • 2(7) c. Arc length of = 360° 12.22 centimeters In parts (a) and (b) in Example 2, note that the arcs have the same measure but different lengths because the circumferences of the circles are not equal.**Ex. 3: Tire Revolutions**• The dimensions of a car tire are shown. • To the nearest foot, how far does the tire travel when it makes 8 revolutions?**Assignment**p. 214 (1-10)