Geometry 11.4 Circumference and Arc Length
Geometry 11.4 Circumference and Arc Length. July 2, 2015Geometry 11.4 Circumference and Arc Length2 Goals Find the circumference of a circle. Find.
Dec 21, 2015
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Geometry
11.4 Circumference and Arc Length
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
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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.
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Semicircle
Half of a circle. Its measure is 180. Its length is one-half the
circumference.
Converting Degrees to Radians
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Practice
A circle is 360 degrees. How many radians does that equal?
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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
How many radians are in a semicircle?
April 19, 2023 Geometry 11.4 Circumference and Arc Length 10
Radians to Degrees
April 19, 2023 Geometry 11.4 Circumference and Arc Length 11
Practice
April 19, 2023 Geometry 11.4 Circumference and Arc Length 12
Practice
April 19, 2023 Geometry 11.4 Circumference and Arc Length 13
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.
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Example Find the length of AB.
A
B5
80L
802 (5) 360L
Write the proportion:
Length of Arc
Circumference of circle
Central Angle
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Solve the proportion
802 (5) 360
210 9
9 20
206.98
9
L
L
L
L
A
B5
80L6.98
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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
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Problem 1
An indoor track at a gym has the design below. What is the length of the entire track?
100 ft
40 ft
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Problem 1 Solution
The ends make one circle.
100 ft
40 ft
The diameter is 40 ft.
C = (40)
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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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Summary
The length of an arc on a circle is proportional to the measure of the arc and to the central angle.
A semicircle has 180 and it’s length is half the circumference.
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