CK-12 Geometry Concepts

10.9. Arc Length http://www.ck12.org

Example B

The arc length ofAB̂= 6 πand is^14 the circumference. Find the radius of the circle.

If 6πis^14 the circumference, then the total circumference is 4( 6 π) = 24 π. To find the radius, plug this into the
circumference formula and solve forr.

24 π= 2 πr

12 =r

Example C

Find the measure of the central angle orPQ̂.

Let’s plug in what we know to the Arc Length Formula.

15 π=

mPQ̂

360 ◦

· 2 π( 18 )

15 =

mPQ̂

10 ◦

150 ◦=mPQ̂

Watch this video for help with the Examples above.

MEDIA

Click image to the left for more content.

CK-12 Foundation: Chapter10ArcLengthB

Concept Problem Revisited

In the picture below, the top piece of pizza is if it is cut into 8 pieces. Therefore, for^18 of the pizza, one piece would
have^448 ≈ 5. 5 inchesof crust. The bottom piece of pizza is if the pizza is cut into 10 pieces. For 101 of the crust, one
piece would have^4410 ≈ 4. 4 inchesof crust.

Vocabulary

Circumferenceis the distance around a circle. Arc lengthis the length of an arc or a portion of a circle’s
circumference.

Guided Practice

Find the arc length ofPQ̂in

⊙

A. Leave your answers in terms ofπ.