Geometry Circumference and Arc Length Powerpoint PPT

1. 11.1 Circumference and Arc
Length
Objective: To find arc lengths and
other measures

2. Theorem 11.1
Circumference of a Circle:
r
C
d
C 
 2
or 


4. Arc Length Corollary
d


 0
360
measure
arc
length
arc
In a circle, the ratio of the length of a given
arc to the circumference is equal to the ratio
of the measure of the arc to 360o.
Vocabulary:
An arc length is a portion of the circumference
of a circle.
0
360
measure
arc
r
2
AB
of
length
arc


or

5. REMEMBER!!!
 Arc Length and Arc Measure are
NOT the same!

6. Examples
r
C 
2

C = 2(3.14)(7)
C = 43.96
d
C 

C = (3.14)(20)
C = 62.8
r
C 
2

48 = 2(3.14)r
48 = 6.28r
7.64 = r

7. Examples
r
C 
2

r

2
36 
4.
r


2
36
5. d
C 

d


29
d
feet 

29
r
meters 

18
6. d
C 

26


C
inches
C 
26

7. r
C 
2

)
15
(
2

C
cm
C 
30


8. Examples 0
360
measure
arc
r
2
AB
of
length
arc


360
90
)
7
)(
14
.
3
(
2

x
4
1
96
.
43

x
96
.
43
4 
x
99
.
10

x
360
120
)
6
)(
14
.
3
(
2

x
3
1
68
.
37

x
68
.
37
3 
x
56
.
12

x
360
45
)
12
)(
14
.
3
(
2

x
8
1
36
.
75

x
36
.
75
8 
x
42
.
9

x

9. 11. MACB = 360-40 = 320o
360
320
)
4
)(
14
.
3
(
2

x
13.
9
8
12
.
25

x
96
.
200
9 
x 33
.
22

x
15. mACB = 320 mBC = 320/2 = 160
mABC = 160 + 40 = 200o

10. Examples
2
40
360
.
12

160
2
320

360
160
)
4
)(
14
.
3
(
2

x
14.
9
4
12
.
25

x
48
.
100
9 
x 16
.
11

x
16.
360
200
)
4
)(
14
.
3
(
2

x
9
5
12
.
25

x
6
.
125
9 
x 96
.
13

x

11. Examples
360
135
)
10
)(
14
.
3
(
2

x
8
3
8
.
62

x
4
.
188
8 
x
55
.
23

x
0
360
measure
arc
r
2
AB
of
length
arc


360
60
2
15

r

6
1
15

C
90

C
360
90
2
18

r


4
1
9

r
36

r

12. Examples
Perimeter = C + 2(15)
P = (3.14)(9) + 2(15)
P = 28.26 + 30
P = 58.26
P = 2(3.14)(2) + 3(4)
Perimeter = C + 3(4)
P = 12.56 + 12
P = 24.56

13. Examples
C = (3.14)(4.5)
C = 14.13 inches
14.13 x 150 = 2,119.5 inches
2,119.5 inches/12 = 176.625 feet