1. Sec. 10.6 Circumference and Arc Length p.649
Objectives: Find circumference and arc length.
Vocabulary: circumference, arc length, radius, diameter, measure of an arc

2. Review of Circles
Find each measure. RT
54

3. Review circumference (distance around) of a circle:
C = πd or
C = 2πr

4. a. C = 2 πr = 2 π 9 = 18 π 56.55 cm Find the indicated measures.
Circumference of a circle
with radius 9 centimeters a.
C = 2 πr
= 2 π 9
= 18 π
56.55 cm

5. Find the indicated measures.
Radius of a circle with
circumference 26 meters
C = 2 πr =
2 πr 26 = 26 2π r r
4.14

6. Find the circumference of a circle with diameter 5 inches.
Find the diameter of a circle with circumference 17 feet.
about in.
about 5.41 feet

7. The length of an arc is a fraction of the circumference of the circle.

8. Find the length of each red arc.
Arc length = 2πr (m˚/360˚)
60°
360° = a.
Arc length of AB
2π(8)
≈ 8.38 centimeters

9. Find the length of each red arc.b.
Arc length = 2πr (m˚/360˚)
60°
360° = b.
Arc length of EF
2π(11)
≈ centimeters

10. Find the length of each red arc.
Arc length = 2πr (m˚/360˚)
2π(11)
120°
360° = c.
Arc length of GH
≈ centimeters

11. Find each arc length. Give answers to the nearest hundredth.FG
 cm
Arc length = 2πr (m˚/360˚)

12. Find each arc length. Give answers to the nearest hundredth.
an arc with measure 62 in a circle with radius 2 m
Arc length = 2πr (m˚/360˚)
 2.16 m

13. Find each arc length. Give your answer rounded to the nearest hundredth.GH
 4.19 m

14. Find each measure. Give answers to the nearest hundredth.
length of NP
 7.85 in.

15. Use arc lengths to find measures
1. Circumference C of Z
Arc length = 2πr (m˚/360˚)
Arc length = C (m˚/360˚)
Arc length of XY 1.
360°
m XY = C
4.19 = C(40/360)
(360/40) 4.19 = C(40/360)(360/40)
37.71 = C

16. Arc length = 2πr (m˚/360˚) Find the indicated measure. 2. m RS
Arc length of RS
(2 r)
360° 2.
m RS = 44
(2 (15.28))
m RS
360° = 44
(2 (15.28))
360°
= m RS
15840
( )
= m RS
165°
m RS

17. Arc length = 2πr (m˚/360˚) Find the indicated measure. 3. Length of PQ
Arc length = πd (m˚/360˚)
about 5.89 yd

18. Arc length = C (m˚/360˚) 61.26= (C) 270˚ 360˚ 61.26(360) = C (270˚)
4. Circumference of N N.
Arc length = C (m˚/360˚)
61.26= (C) 270˚
360˚
81.68 m
61.26(360) = C (270˚)

19. Arc length = 2πr (m˚/360˚) 10.5= 2πr (150˚/360˚)
5. Radius of G
Arc length = 2πr (m˚/360˚)
10.5= 2πr (150˚/360˚)
10.5(360) = 2πr (150˚)
about 4.01 ft.