11.4 Circumference and Arc Length

Report
11.4 Circumference and Arc Length
2/17/2011
Objectives
Find the circumference of a circle and the
length of a circular arc.
 Use circumference and arc length to solve
real-life problems.

Finding circumference and arc length

The circumference of a circle is the
distance around the circle.

For all circles, the ratio of the
circumference to the diameter is the
same. This ratio is known as  or pi.
Theorem 11.6: Circumference of a
Circle

The circumference C
of a circle is C = d or
C = 2r, where d is
the diameter of the
circle and r is the
radius of the circle.
diameter d
Ex. 1: Using circumference

Find
(Round decimal answers to two decimal places)
◦ (a) the circumference of a circle with radius 6
centimeters and
◦ (b) the radius of a circle with circumference
31 meters.
What’s the difference??

Find the exact radius of a circle with
circumference 54 feet.

Find the radius of a circle with
circumference 54 feet.
Extra Examples
Write below previous box

Find the exact circumference of a circle
with diameter of 15.

Find the exact radius of a circle with
circumference of 25.
And . . .

An arc length is a portion of the
circumference of a circle.

You can use the measure of an arc
(in degrees) to find its length (in
linear units).
Finding the measure of an Arc Length

In a circle, the ratio
of the length of a
given arc to the
circumference is
equal to the ratio of
the measure of the
arc to 360°.
A
P
B

Arc length of AB

=
m AB
360°
• 2r
More . . .

The length of a
semicircle is half the
circumference, and
the length of a 90° arc
is one quarter of the
circumference.
½ • 2r
d
r
¼ • 2r
Ex. 2: Finding Arc Lengths

Find the length of each arc.
E
a.
5 cm
A
50°
c.
7 cm
100°
B
F
Ex. 2: Finding Arc Lengths

Find the length of each arc.
b.
7 cm
C
50°
D
Ex. 2: Finding Arc Lengths

Find the length of each arc.
E
c.
7 cm
100°
F
Ex. 2: Finding Arc Lengths

Find the length of each arc.
a.

a. Arc length of
AB
5 cm
# of °
=
A
50°
B

a. Arc length of
AB
360°
50°
=
• 2r
• 2(5)
360°
 4.36 centimeters
Ex. 2: Finding Arc Lengths

Find the length of each arc.
b.

b. Arc length of
CD
7 cm
C
50°

b. Arc length of
CD
D
# of °
=
360°
50°
=
• 2r
• 2(7)
360°
 6.11 centimeters
Ex. 2: Finding Arc Lengths

Find the length of each arc.
E
c.

c. Arc length of
EF
7 cm
100°

c. Arc length of
EF
F
# of °
=
360°
100°
=
• 2r
• 2(7)
360°
 12.22 centimeters
In parts (a) and (b) in Example 2, note that the
arcs have the same measure but different
lengths because the circumferences of the
circles are not equal.
Ex. 3: Tire Revolutions
The dimensions of a car
tire are shown.
 To the nearest foot, how
far does the tire travel
when it makes 8
revolutions?

Assignment
P. 214 (1-10)

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