Take note Theorem 10-10: Arc Length

The length of an arc of a circle is the product of the ratio

measure of the arc 360 fraction measure of the arc , over 360 end fraction  and the circumference of the circle.

length of  A B ⌢ = m A B ⌢ 360 ⋅ 2 π r   = m A B ⌢ 360 ⋅ π d table with 2 rows and 2 columns , row1 column 1 , length of . modified eh b with frown above , column 2 equals . fraction m , modified eh b with frown above , over 360 end fraction . dot 2 pi r , row2 column 1 , , column 2 equals . fraction m , modified eh b with frown above , over 360 end fraction . dot pi d , end table

Problem 4 Finding Arc Length

What is the length of each arc shown in red? Leave your answer in terms of π . pi .

1. 

   length of   X Y ⌢ = m X Y ⌢ 360 ⋅ π d Use a formula for arc length.   = 90 360 ⋅ π ( 16 ) Substitute.   = 4 π  in. Simplify. table with 3 rows and 3 columns , row1 column 1 , length of . , modified x y with frown above , column 2 equals . fraction m , modified x y with frown above , over 360 end fraction . dot pi d , column 3 cap use a formula for arc length. , row2 column 1 , , column 2 equals , 90 over 360 , dot pi open 16 close , column 3 cap substitute. , row3 column 1 , , column 2 equals 4 pi , in. , column 3 cap simplify. , end table

2. 

   length of  X P Y ⌢ = m X P Y ⌢ 360 ⋅ 2 π r   = 240 360 ⋅ 2 π ( 15 )   = 20 π cm table with 3 rows and 2 columns , row1 column 1 , length of . modified x p y with frown above , column 2 equals . fraction m . modified x p y with frown above , over 360 end fraction . dot 2 pi r , row2 column 1 , , column 2 equals , 240 over 360 , dot 2 pi open 15 close , row3 column 1 , , column 2 equals 20 pi cm , end table

✓ Got It?

4. What is the length of a semicircle with radius 1.3 m? Leave your answer in terms of π . pi .