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 = d C = (12) 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 a PORTION of the circumference Don’t confuse arc length with arc measure The length of an arc is in linear units. (such as ft, cm, etc.) – it is dependent on the size of the circle The measure of an arc is in degrees (we have done this already at the beginning of the unit) – it is NOT dependent on the size of the circle

6. Arc Length Percentage of the circle that your part is Will be in degrees

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

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

9. Ex: Sometimes there are 2 steps - Find the length of LPM. ( C L M 100o 1 0 m P

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

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

12. Radians Radians are another way to measure angles A radian is the ratio of the arc length to the radius

13. Converting Radians 2π radians = 360 o Degrees = radians * 360/2 π Radians = degrees * 2 π/360

14. Arc length with radians If we rearrange the formula for radians, it is easy to find arc length if given radians

15. 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?