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Chapter 7 Lesson 6

Chapter 7 Lesson 6. Objective: To find the circumference and arc length. The circumference of a circle is the distance around the circle. The number pi ( π ) is the ratio of the circumference of a circle to its diameter. Theorem 7-13 Circumference of a Circle

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Chapter 7 Lesson 6

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  1. Chapter 7 Lesson 6 Objective: To find the circumference and arc length.

  2. The circumference of a circle is the distance around the circle. The number pi (π) is the ratio of the circumference of a circle to its diameter. Theorem 7-13Circumference of a Circle The circumference of a circle is π times the diameter.

  3. Circles that lie in the same plane and have the same center are concentric circles.

  4. Example 1: Concentric Circles A car has a turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. In completing the (outer) turning circle, how much farther does a tire travel than a tire on the concentric inner circle? circumference of outer circle = C = 2πr = 2π(16.1) = 32.2π To find the radius of the inner circle, subtract 4.7 ft from the turning radius. radius of the inner circle = 16.1 − 4.7 = 11.4 circumference of inner circle = C = 2πr = 2π(11.4) = 22.8π The difference in the two distances is 32.2π − 22.8π, or 9.4π. A tire on the turning circle travels about 29.5 ft farther than a tire on the inner circle.

  5. The measure of an arc is in degrees while the arc length is a fraction of a circle's circumference. Theorem 7-14Arc Length The length of an arc of a circle is the product of the ratio                  and the circumference of the circle. length of    =      • 2πr

  6. Example 2:Finding Arc Length Find the length of each arc shown in red. Leave your answer in terms of π.

  7. Example 3:Finding Arc Length Find the length of a semicircle with radius of 1.3m. Leave your answer in terms of π.

  8. B • 18 cm • 150° • M D • A Example 4:Finding Arc Length Find the length of ADB in terms of π.

  9. Congruent arcs are arcs that have the same measure and are in the same circle or in congruent circles.

  10. Assignment pg. 389-392 #27-39; 55-59

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