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April 19, 2023 Geometry 11.4 Circumference and Arc Length 2
Goals
Find the circumference of a circle. Find the length of an arc. Solve problems using circumference
and arc length. Conversions involving radians
April 19, 2023 Geometry 11.4 Circumference and Arc Length 3
Circumference
The circumference is the distance around a circle.
April 19, 2023 Geometry 11.4 Circumference and Arc Length 4
Circumference
You can find the circumference if you know the diameter (d) or the radius (r) of the circle.
2
C d
C r
April 19, 2023 Geometry 11.4 Circumference and Arc Length 5
Example
Find the circumference of a circle with a radius of 8.
2 (8)
16
50.24
C
This is the circumference “in terms of pi”.
When computing C in decimal, use 3.14 or the pi button.
April 19, 2023 Geometry 11.4 Circumference and Arc Length 6
Semicircle
Half of a circle. Its measure is 180. Its length is one-half the
circumference.
Practice
A circle is 360 degrees. How many radians does that equal?
April 19, 2023 Geometry 11.4 Circumference and Arc Length 8
Practice
A circle is 360 degrees. How many radians does that equal?
Think about when we inscribed a hexagon in a circle.
April 19, 2023 Geometry 11.4 Circumference and Arc Length 9
April 19, 2023 Geometry 11.4 Circumference and Arc Length 14
Arc Length
The ratio of the length of an arc to the circumference of a circle is equal to the ratio of the measure of the arc to 360.
A
B
Arc Length of AB2 360
mABr
Recall: the measure of the arc is equal to the central angle that intercepts it.
April 19, 2023 Geometry 11.4 Circumference and Arc Length 15
Example Find the length of AB.
A
B5
80L
802 (5) 360L
Write the proportion:
Length of Arc
Circumference of circle
Central Angle
April 19, 2023 Geometry 11.4 Circumference and Arc Length 16
Solve the proportion
802 (5) 360
210 9
9 20
206.98
9
L
L
L
L
A
B5
80L6.98
April 19, 2023 Geometry 11.4 Circumference and Arc Length 17
Your Turn Find the length of AB
A
B8
25
252 (8) 360
2516 360
360 400
109
3.43
9
40060
x
x
x
x
x
x
April 19, 2023 Geometry 11.4 Circumference and Arc Length 18
Example
The length of AB is 25 and the radius is 10. Find the mAB.
A
B
10
x25
252 (10) 360
20 9000
9000 45020
143.2
x
x
x
x
April 19, 2023 Geometry 11.4 Circumference and Arc Length 19
Problem 1
An indoor track at a gym has the design below. What is the length of the entire track?
100 ft
40 ft
April 19, 2023 Geometry 11.4 Circumference and Arc Length 20
Problem 1 Solution
The ends make one circle.
100 ft
40 ft
The diameter is 40 ft.
C = (40)
April 19, 2023 Geometry 11.4 Circumference and Arc Length 21
Problem 1 Solution
100 ft
40 ft
Add 200 for the straight segments.
Perimeter = 40 + 200 ft
Or, 325.66 ft.
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