Chapter 7 Lesson Chapter 7 Lesson 66

Objective:Objective: To find the To find the circumference and arc length.circumference and arc length.

The circumference of a circle is the distance around the circle.

The number pi (π) is the ratio of the circumference of a circle to its diameter.

Theorem 7-13  Circumference of a CircleThe circumference of a circle is π times the diameter.

rC

or

dC

2

Circles that lie in the same plane and have the same center are concentric circles.

A car has a turning radius of 16.1 ft. The distance between the two A car has a turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. In completing the (outer) turning circle, how front tires is 4.7 ft. In completing the (outer) turning circle, how

much farther does a tire travel than a tire on the concentric inner much farther does a tire travel than a tire on the concentric inner circle?circle?

circumference of outer circle = C = 2πr = 2π(16.1) = 32.2π

To find the radius of the inner circle, subtract 4.7 ft from the turning radius. radius of the inner circle = 16.1 − 4.7 = 11.4 circumference of inner circle = C = 2πr = 2π(11.4) = 22.8π

The difference in the two distances is 32.2π − 22.8π, or 9.4π.

                                                                                                                            A tire on the turning circle travels about 29.5 ft farther than a tire on the inner

circle.

Example 1:Concentric Circles

The measure of an arc is in degrees while the arc length is a fraction of a circle's circumference.

Theorem 7-14Theorem 7-14  Arc LengthThe length of an arc of a circle is the product of the ratio

                 and the circumference of the circle. length of    =      • 2πr

Example 2: Finding Arc Length

Find the length of each arc shown in red. Leave your answer in terms of π.                                                                            

Example 3: Finding Arc Length

Find the length of a semicircle with radius of 1.3m. Leave Find the length of a semicircle with radius of 1.3m. Leave your answer in terms of your answer in terms of π.π.

r2360180

)3.1(221

6.221

3.1

Example 4: Finding Arc Length

Find the length of ADB in terms of π.π.

••

•

A

B

M D•150°18 cm

rmADB 2360

)18(2360210

21

Congruent arcs are arcs that have the same measure Congruent arcs are arcs that have the same measure andand are in the same circle or in congruent circles. are in the same circle or in congruent circles.

AssignmentAssignment

pg. 389-392 pg. 389-392 #27-39; 55-59#27-39; 55-59