
Understand Radian Measure
Presentation
•
Mathematics
•
9th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
16 Slides • 17 Questions
1
16.2 Arc Length and Radian Measure
Goal: I can find the arc length, radius/diameter, or central angle of a circle.
2
3
Arc Length (COPY NOTES)
Arc Length is the length of a portion of the circumference.
To find this we multiply the circumference by the fraction of the circle the arc subtends.
The fraction of the circle is determined by dividing the central angle by 360.
4
(NOTES)Example 1: Find length of minor arc AB.
Arc Length = 2πr(360central angle)
r = 12; central angle = 45
Arc Length = 2π(12)(36045)
Arc Length = 3π or 9.42
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(NOTES) Example 2:
A pizza has been cut into 10 equal pieces. The outer edge of the crust of one piece measures 7 units. Find the diameter of the pizza to the nearest whole number.
Arc Length = 7 units; Central angle = (360/10) = 36
7=2πr(36036)
7=51πr
r=11.140846
The diameter of the pizza is 22 units.
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Fill in the Blanks
Type answer...
7
8
Multiple Choice
Find the arc length of the bold arc. Leave π in your answer.
S=360°θ2πr leave π in your answer.
5688π ft
15.8π ft
150.4π ft
54,150 ft
9
10
Multiple Choice
Find the arc length. Leave your answer in terms of π.
S=360°θ2πr leave the π in the answer.
7π/4
7π/2
π/8
45π
11
Multiple Choice
When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.
40
35
55
69
12
13
Multiple Choice
An ____ is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.
adjacent
arc
algorithm
area
14
Multiple Choice
What is the formula for?
arc length
area of a sector
area of a segment
arc measure
15
Multiple Choice
Find the arc length of the bolded arc in the picture. (Use 3.14 for π )
S=360θ⋅2⋅π⋅r
A
B
C
D
16
Multiple Choice
In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree. (Use 3.14 for π )
90
60
55
113
17
18
19
20
21
Multiple Choice
What formula is this?
Arc length when θ is in radians
Arc length when θ is in degrees
Sector Area when θ is in radians
Sector Area when θ is in degrees
22
Multiple Choice
A central angle measures 4.5 radians and has an arc of 35 inches. What is the radius of the circle?
7.78 inches
8.21 inches
157.5 inches
7 inches
23
24
Multiple Choice
Find the arc length.
7 cm
28π cm
7π cm
28 cm
25
Multiple Choice
12π cm
27π cm
12 cm
27 cm
26
Multiple Choice
Find the arc length.
3π/4 ft
39π/4 ft
13π/4 ft
4π/13 ft
27
28
Multiple Choice
What is 225 degrees in radians?
7π/4
5π/4
3π/4
5π/3
29
30
Multiple Choice
Convert 150⁰ to radians.
65π
43π
67π
32π
31
Multiple Choice
What is 7π/4 radians in degrees?
MULTIPLY BY (180/π)
300
135
315
45
32
33
Multiple Choice
Convert 4π radians to degrees
90⁰
45⁰
60⁰
30⁰
16.2 Arc Length and Radian Measure
Goal: I can find the arc length, radius/diameter, or central angle of a circle.
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