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Circumference & Arc Length

Circumference & Arc Length. Circumference. T he distance around a circle C = 2  r or d. Ex : Find the circumference of a circle with a diameter of 12 cm. . C = 2 r C = 2(6) C = 12 C = 37.70 cm * If asked for an exact answer, the result would look like this. cm.

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Circumference & Arc Length

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  1. Circumference & Arc Length

  2. Circumference • The distance around a circle • C = 2r or d

  3. Ex: Find the circumference of a circle with a diameter of 12 cm. C = 2r C = 2(6) C = 12 C = 37.70 cm * If asked for an exact answer, the result would look like this. cm

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

  5. Arc Length • Arc Length is PART of the circumference – when you only want to go part way around the circle • Don’t’ confuse arc length with arc measure • The length of an arc is in linear units. (such as ft, cm, etc.) • The measure of an arc is in degrees (we have done this already at the beginning of the unit)

  6. Arc Length ( • To find the length of AB : Will be in degrees Percentage of the circle that your part is

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

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

  9. Ex: Sometimes there are 2 steps - Find the length of LPM. ( L M 100o 10 m C P

  10. Ex: Find the radius 5.7 cm L M 125o C P

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

  12. Radians • Radians are another way to measure angles • Angle measures in degrees have degree symbol, angle measures in radians do not • A radian is the ratio of the arc length to the radius • 2π radians = 360o • To convert from radians to degrees, multiply by 360/2π • To convert from degrees to radians, multiply by 2π/360 • Using this information and plugging back into equation for arc length – if you know the radian measure of an angle

  13. Examples • Convert to radians • Convert to degrees • If an angle has a measure of π radians and the radius of the circle is 8 inches, what is the arc length?

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