This document contains notes and examples about arc lengths and circumferences of circles. It defines circumference as C = 2πr and arc length as a fraction of the circumference based on the central angle. Several word problems are provided that require calculating arc lengths, circumferences, radii, or diameters given portions of circles or central angles.

1. 11.4 Arc Lengths March 20, 2013
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 ft 2
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
Mar 7­10:19 AM
HW pg. 749 #4­26 evens 1

2. 11.4 Arc Lengths March 20, 2013
11.4 Circumference & Arc Length
Circumference of a Circle:
C = 2πr (Twinkle­twinkle)
The circumference of a circle is 28 What is the area of the circle?
π.
Mar 7­10:29 AM
HW pg. 749 #4­26 evens 2

3. 11.4 Arc Lengths March 20, 2013
Arc Length: fraction of a circle's circumference
xo where x = the arc measure
360 *circumference
D
o
M
0
yd
28
6.5
C
C B
4i
n
o
60
A N
Length AB = ____ Length minor arc
MN = ____
Mar 7­11:51 AM
HW pg. 749 #4­26 evens 3

4. 11.4 Arc Lengths March 20, 2013
M
cm
22
P
Q
N
0
50 Arc QN = 60 o
Find the length of arc NM.
Q M
diameter = 9 ft
Length of QM = _______
The length of AB is 6 π. Find the radius.
120 o
A
r
B
Mar 7­12:03 PM
HW pg. 749 #4­26 evens 4

5. 11.4 Arc Lengths March 20, 2013
Mar 21­7:30 AM
HW pg. 749 #4­26 evens 5

6. 11.4 Arc Lengths March 20, 2013
11.4 HW pg. 749 #4­26 evens
Mar 7­10:40 AM
HW pg. 749 #4­26 evens 6