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10.9 Circumference and Arc Length

Learn to calculate circle perimeter and arc length, key to geometry. Examples demonstrate methods for real-world applications.

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10.9 Circumference and Arc Length

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  1. 10.9 Circumference and Arc Length After studying this section, you will be able to determine the circumference of a circle and the length of an arc.

  2. Circumference Definition The circumference of a circle is its perimeter Postulate Example 1 Find, to the nearest hundredth, the circumference of a circle whose radius is 5.37 in.

  3. Length of an Arc Arc length is a linear measurement. The length of an arc depends both on the arc’s measure and on the circumference of its circle. Example 2 Find the length of a 40 arc of a circle with an 18 cm radius.

  4. Theorem The length of an arc is equal to the circumference of its circle times the fractional part of the circle determined by the arc where r is the radius and is measured in degrees.

  5. Example 3 Find the radius of a circle whose circumference is

  6. Example 4 • Find the length of each arc of a circle with a 12 cm radius. • A 30 arc • A 105 arc

  7. Example 5 • The diameter of a bicycle wheel (including the tire) is 70 cm. • How far will the bicycle travel if the wheel rotates 1000 times? (to the nearest meter) • How many covered revolutions will the wheel make if the bicycle travels 15 m.

  8. Summary How can circumference be used in everyday life? Homework: Worksheet 10.9

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