This document contains notes and examples for calculating circumference and arc length of circles. It includes the formulas for circumference (C=2πr) and calculating arc length as a proportion of the total circumference. There are multiple word problems worked through that apply these formulas to find missing values like radii and arc lengths. Diagrams accompany most of the problems to illustrate the geometry involved.

1. 11.4 Circumference & Arc Length March 05, 2012
Bellwork
Figure I ~ Figure II. Find the ratio of the perimeters and the
ratio of the areas. Then find the unknown area.
Ratio of perimeters: 4:3;
ratio of areas: 16:9;
Unknown Area:33.75 ft2
2. Rectangle I ~ Rectangle II.
In Rectangle I, the length is 20 feet & the perimeter is 64 feet.
In Rectangle II, the width is 8 yards.
Find the ratio of the area of Rectangle I to the area of Rectangle II.
144 : 576
1 : 4
HW pg. 747 #4­26 evens 1

2. 11.4 Circumference & Arc Length March 05, 2012
11.4 Circumference & Arc Length
Circumference of a Circle:
C = 2πr (Twinkle­twinkle)
The circumference of a circle is 28 π. What is the area of the circle?
HW pg. 747 #4­26 evens 2

3. 11.4 Circumference & Arc Length March 05, 2012
Arc Length: fraction of a circle's circumference
xo
360 *circumference
where x = the arc measure
D
0o
M
28
yd
6.5
C
C B
4i
o
n
60
A N
Length AB = ____ Length minor arc
MN = ____
HW pg. 747 #4­26 evens 3

4. 11.4 Circumference & Arc Length March 05, 2012
M
cm
22
P
Q
N
0
50 Arc QN = 60o
Find the length of arc NM.
Q M
diameter = 9 ft
Length of QM = _______
The length of AB is 6π. Find the radius.
120 o
A
r
B
HW pg. 747 #4­26 evens 4

5. 11.4 Circumference & Arc Length March 05, 2012
HW pg. 747 #4­26 evens 5

6. 11.4 Circumference & Arc Length March 05, 2012
11.4 HW pg. 749 #4­26 evens
HW pg. 747 #4­26 evens 6