What is arc length?

What is a sector?

How do you find arc length?

How do you find the area of a sector?

Arc Length and Sectors

Arc Lengths

Arc lengths are the pieces of the circumference cut by central angles.

Arc lengths are measured in units of measure like inches and centimeters.

Can arc length be measured with a ruler?

Arc length

A

B

Sector AreaSector area is the

wedge-shaped interior regions of a circle formed by central angles.

Definition

A sector of a circle is a region formed by two radii and an arc of circle. ABC is a sector of ּסB

A

BC

is a central angle of ּסK

Find the arc length (L) of JL to the nearest tenth.

C = 2 π r (circumference)

The arc covers 125° out of a total of 360° or

JKL

JK

L

125° 12 cm

360

125

2.26360

125122 L

Formula for Arc Length

360

degreesarc2 rL

is a central angle of ּסK

The arc covers 125° out of a total of 360° or

JK

L

125° 12 cm

2A r

360

125

Find the area of sector JKL to the nearest tenth.

JKL

1.157360

12512A 2

Formula for Sector Length

360

degreesarcA 2 r

In ּסC, mAB = 103° and AC = 20 in.

Find the area of sector ACB to the nearest tenth.

360

10320A 2

A

B

C

103°

20 in

Find the length of arc AB to the nearest tenth.

359.5

360

103202L 36.0

If the circumference of a circle is 21π, what is the length of a 30° arc?

B

A

C

30°

360

3021 L

5.54

7

12

21

12

121L

• What is an arc length?

Arc lengths are the pieces of the circumference cut by central angles.

• What is a sector?

Sector area is the wedge-shaped interior regions of a circle formed by central angles.

• How do you find arc length?

• How do you find the area of a sector?

360

degreesarc2L r

360

degreesarcA 2 r