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.