http://www.ck12.org Chapter 10. Perimeter and Area
10.9 Arc Length
Here you’ll learn how to find the length of an arc.
What if you wanted to find the "length" of the crust for an individual slice of pizza? A typical large pizza has a
diameter of 14 inches and is cut into 8 or 10 pieces. If the "length" of the entire crust is the circumference of the
pizza, find the "length" of the crust for one piece of pizza when the entire pizza is cut into a) 8 pieces or b) 10 pieces.
After completing this Concept, you’ll be able to answer these questions.
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Click image to the left for more content.CK-12 Foundation: Chapter10ArcLengthA
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Click image to the left for more content.Brightstorm:ArcLength
Guidance
One way to measure arcs is in degrees. This is called the “arc measure” or “degree measure.” Arcs can also be
measured in length, as a portion of the circumference.Arc lengthis the length of an arc or a portion of a circle’s
circumference. The arc length is directly related to the degree arc measure.
Arc Length Formula:Ifdis the diameter orris the radius, the length ofAB̂=m 360 AB̂◦·πdorm 360 AB̂◦· 2 πr.
Example A
Find the length ofPQ̂. Leave your answer in terms ofπ.
In the picture, the central angle that corresponds withPQ̂is 60◦. This means thatmPQ̂= 60 ◦as well. So, think of
the arc length as a portion of the circumference. There are 360◦in a circle, so 60◦would be^16 of that
( 60 ◦
360 ◦=
1
6)
.
Therefore, the length ofPQ̂is^16 of the circumference.
length o fPQ̂=1
6
· 2 π( 9 ) = 3 π