Circumference • The distance around a circle • C = 2 r or d
Ex: Find the circumference of a circle with a diameter of 12 cm. C = d C = (12) C = 12 cm C = 37. 70 cm * If asked for an exact answer, the result would look like this.
Ex: Find the radius of a circle with a circumference of 52 in. C = 2 r 52/2 = r 8. 28 in. r
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
Arc Length Will be in degrees Percentage of the circle that your part is
( Ex: Find the length of JK. C 60 o J 16 in. K
( Ex: Find the m LM. 16. 76 in. L . n i 8 M C (
( Ex: Sometimes there are 2 steps - Find the length of LPM. L M 100 o C P 10 m
Ex: Find the radius 5. 7 cm L M 125 o C P
Ex: Find the circumference of circle C. R 10. 2 cm 45 o C S
Radians • Radians are another way to measure angles • A radian is the ratio of the arc length to the radius
Arc length with radians • If we rearrange the formula for radians, it is easy to find arc length if given radians
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?