11.4 circumference and arc length 2/17/2011. objectives find the circumference of a circle and the...
TRANSCRIPT
11.4 Circumference and Arc Length
2/17/2011
ObjectivesFind 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 lengthThe 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 CircleThe
circumference C of a circle is C = d or C = 2r, where d is the diameter of the circle and r is the radius of the circle.
diameter d
Ex. 1: Using circumferenceFind
(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 boxFind 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 LengthIn 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°.
P
B
A
Arc length of =360°
• 2r AB
mAB
More . . .
The length of a semicircle is half the circumference, and the length of a 90° arc is one quarter of the circumference.
½ • 2r
r¼ • 2r
d
Ex. 2: Finding Arc Lengths
Find the length of each arc.
5 cm
B
A
50°
a. 7 cm
F
E
100°c.
7 cm
D
C
b.
50°
Ex. 2: Finding Arc LengthsFind the length of each arc.
7 cm
F
E
100°
c.
Ex. 2: Finding Arc LengthsFind the length of each arc.
Ex. 2: Finding Arc Lengths
AB
Find the length of each arc.
5 cm
B
A
50°
a.
a. Arc length of = AB 50°
360°• 2(5)
a. Arc length of = # of °
360°• 2r
4.36 centimeters
Ex. 2: Finding Arc LengthsFind the length of each arc.
7 cm
D
C
50°
b. b. Arc length of = CD # of °
360°• 2r
b. Arc length of = CD 50°
360°• 2(7)
6.11 centimeters
Ex. 2: Finding Arc Lengths
EF
Find the length of each arc.
7 cm
F
E
100°
c. c. Arc length of = # of °
360°• 2r
c. Arc length of = EF 100°
360°• 2(7)
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 RevolutionsThe dimensions of a
car tire are shown.To the nearest foot,
how far does the tire travel when it makes 8 revolutions?
P. 214 (1-10)
Assignment