6.7 Circumference & 6.7 Circumference & Arc LengthArc Length

NotesNotes

CircumferenceCircumference

The distance around a circle.The distance around a circle.

Do you remember the formula???Do you remember the formula???

C = 2C = 2r or C = r or C = dd

* Always use the * Always use the button on your button on your calculator, calculator, NOTNOT 3.14!!! 3.14!!!

C = 2C = 2rr

C = 2C = 2(6)(6)

C = 12C = 12 cm cm

C = 37.70 cmC = 37.70 cm

* If you are asked * If you are asked for the for the exactexact value leave your value leave your answer in terms answer in terms of of . It will look . It will look like this!!!like this!!!

Ex 1Ex 1: Find the circumference of a : Find the circumference of a circle with a diameter of 12 cm. circle with a diameter of 12 cm. (Round to 2 decimal places.)(Round to 2 decimal places.)

C = C = dd

C = C = (12)(12)

C = 12C = 12C = 37.70 cmC = 37.70 cm

OROR

Ex 2Ex 2: Find the radius of a : Find the radius of a circle with a circumference of circle with a circumference of

52 in.52 in.

C = 2r52 = 2r

8.28 in. r

52= r2π

What if you only want to know the What if you only want to know the length of a piece of the length of a piece of the circumference???circumference???

This is called This is called Arc LengthArc Length

It is a piece of the circumference of circle.It is a piece of the circumference of circle.A

B

Arc Length

Arc Length CorollaryArc Length Corollary

Things to keep in mind when finding arc lengthThings to keep in mind when finding arc length•The The measure of an arcmeasure of an arc is in degrees. is in degrees.•The The length of an arclength of an arc is in linear units. is in linear units.

(such as ft, cm, etc.)(such as ft, cm, etc.)

o

m AB*2πr

360

The length of AB is:The length of AB is:

((

Ex 1: Find the length of JK.Ex 1: Find the length of JK.

((

CC

JJ

KK

6060oo

16 in.16 in.

x 16.76 in.

Your Turn: Find the length of Your Turn: Find the length of AB.AB.

((

AA

BB150150oo

34 34 cm.cm.

length of AB 44.48 in.

Ex 2: Find the m LM.Ex 2: Find the m LM.Notice that we are given the arc length and need to find the Notice that we are given the arc length and need to find the

measure of the arc!!measure of the arc!!

((

CC

LL

16.76 16.76 in.in.

8 in.8 in.

o120.03 =m LM

M

Your Turn: Find the m AB.Your Turn: Find the m AB.

((

CC

BB

18.84 18.84 m.m.

9 in.9 in.

o120 =m LM

A

Ex 3Ex 3: Find the circumference of circle : Find the circumference of circle C.C.

4545oo

10.2 10.2 cmcm

RR

SS

CC

81.6 cm=C

Your TurnYour Turn: Find the circumference of circle : Find the circumference of circle C.C.

200200oo

41.87 41.87 cmcm

AA

BB

CC

C 75.37 cm

Your TurnYour Turn: Find the : Find the radiusradius of circle C.of circle C.READ the directions carefully!!!READ the directions carefully!!!

4545oo

1.57 ft1.57 ftRR

SS

CC

r 2 f t

PracticePractice

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