CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 10. Perimeter and Area

Example 5:Find the length ofPQ̂. Leave your answer in terms ofπ.

Solution:In the picture, the central angle that corresponds withPQ̂ is 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

Arc Length Formula:Ifdis the diameter orris the radius, the length ofAB̂=m 360 AB̂◦·πdorm 360 AB̂◦· 2 πr.

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

Solution: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

Know What? RevisitedThe entire length of the crust, or the circumference of the pizza is 14π≈ 44 in. In the
picture to the right, 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.