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Understanding Circumference and Arc Length of Circles

This guide explains the concepts of circumference and arc length of a circle. The circumference is defined as the distance around a circle, calculated using the formulas C = 2πr or C = πd, where r is the radius and d is the diameter. Important tips include always using the π button on calculators rather than approximating with 3.14. Additionally, we explore how to calculate arc length and its relationship to the circle's circumference, including specific examples to illustrate these concepts in practical terms.

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Understanding Circumference and Arc Length of Circles

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  1. 6.7 Circumference & Arc Length

  2. Circumference • Defn. – the distance around a circle. • Thm. 6.19 – Circumference of a Circle – C = 2r or C = d * Always use the  button on your calculator, NOT 3.14!!!

  3. C = d C = (12) C = 12 C = 37.70 cm C = 2r C = 2(6) C = 12 C = 37.70 cm * If asked to leave your answer in terms of , the result would look like this. Ex: Find the circumference of a circle with a diameter of 12 cm. (Round to 2 decimal places.) OR cm

  4. C = 2r 52 = 2r 52/2 = r 8.28 in.  r C = d 52 = d 52/ = d 16.55 in.  d So, r  16.55/2 r  8.28 in. Ex: Find the radius of a circle with a circumference of 52 in. OR

  5. Arc Length • Defn. – a portion of the circumference of a circle. • The measure of an arc is in degrees. • The length of an arc is in linear units. (such as ft, cm, etc.)

  6. Arc Length Corollary ( • The length of AB is: (

  7. Ex: Find the length of JK. ( ( C 60o 16 in. J K

  8. Arc Length Corollary Observations • The length of a semicircle is ½ the circumference. • The length of a 90o arc is ¼ the circumference. 180o 90o

  9. Ex: Find the m LM. ( ( ( 16.76 in. ( L M 8 in. ( C ( (

  10. Ex: Find the circumference of circle C. ( R ( 10.2 cm S 45o C

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