11.4 11.4 Circumference Circumference and Arc Lengthand Arc Length

Arc of a CircleArc of a Circle

Definitions

Circumference-The enclosing boundary of a curved geometric figure, esp. a circle.

Arc length- A fraction of the circumference

Theorem

The equation of the circumference

πdiameternceCircumfere

radiusnceCircumfere 2

Find the Circumference

Radius 7

7

Find the Circumference

Radius 7

7

14

72

C

C

Find the Arc Length (often called S)

Find the Central angle θ

(the angle whose vertex is at the center),

Then multiply the Circumference by the fraction Central angle

360°

Find the Arc Length

Given a Central angle of 60° and a Radius of 12.

60

12

Find the Arc Length

Given a Central angle of 60° and a Radius of 12.

60

12

4246

1

122360

60

SLengthArc

Find the Central angle

Let R = 8 inches

Length of S = 16.76 inches

Use 3.14 for piS

R

Find the Central angleLet R = 8 inches

Length of S = 16.76 inches. Use 3.14 for pi

S

R

360

24.5075.16

24.50360

75.16

14.382360

75.16

Find the Central angleLet R = 8 inches

Length of S = 16.76 inches. Use 3.14 for pi

S

R

02.120

360

24.50

24.50

36075.16

24.50

360

360

24.5075.16

24.50360

75.16

Find the Circumference

Central Angle 45°

Arc Length 10.245

2.10

Find the Circumference

Central Angle 45°

Arc Length 10.245

2.10

C

C

C

6.818

12.10

360

452.10

Homework

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# 15 – 38, 40

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