geometry b bellwork

Geometry B Bellwork

1) Find the length of the apothem of a regular hexagon given a side length of 18 cm.

7-6 Circle and Arcs

Geometry

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 = 2r,

where d is the diameter of the circle and r is the radius of the circle.

diameter d

Ex. 1: Using circumference

• Find (a) the circumference of a circle with radius 6 centimeters and (b) the radius of a circle with circumference 31 meters. Round decimal answers to two decimal places.

Solution:C = 2r = 2 • • 6 = 12 37.70So, the

circumference is about 37.70 cm.

C = 2r31 = 2r31 = r

4.93 rSo, the radius is

about 4.93 cm.

2

a.b.

ArcsArc- part of a circleSemicircle- half of the circleMinor arc- smaller than a semicircleMajor arc- greater than a semicircle

Identify the following.a.Minor arcs

b.Semicircles

c.Major arcs that contain point A

P

B

A

P

C B

AD

Find the measures of the arcs.

a.DEb.EAc.EBd.ADBe.EBD

P

B

A

P

C

B

AD44°

78°

E

Geometry B Bellwork

2)Find the measures of EB, BDE, ADB.

P

B

A

P

C

B

AD32°

82°

E

Arc Length Theorem• The length of an arc

of a circle is the product of the ratio, measure of the arc

360

and the circumference of a circle.

P

B

A

Arc length of =360°

• 2r m ABAB

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 • 2r

r ¼ • 2r

r

Ex. 2: Finding Arc Lengths

• Find the length of each arc.

5 cm

B

A50°

a.7 cm

D

C

50°

b. 7 cm

F

E

100°c.

Ex. 2: Finding Arc Lengths• Find the length of each arc.

5 cm

B

A50°

a.

a. Arc length of AB = 50°

360°• 2(5)

a. Arc length of AB = # of °

360°• 2r

4.36 centimeters


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


7 cm

F

E

100°

c. c. Arc length of EF = # 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. 4: Comparing Circumferences• Tire Revolutions: Tires

from two different automobiles are shown on the next slide. How many revolutions does each tire make while traveling 100 feet? Round decimal answers to one decimal place.

• Reminder: C = d or 2r.

• Tire A has a diameter of 14 + 2(5.1), or 24.2 inches.

• Its circumference is (24.2), or about 76.03 inches.

Ex. 4: Comparing Circumferences

• Reminder: C = d or 2r.

• Tire B has a diameter of 15 + 2(5.25), or 25.5 inches.

• Its circumference is (25.5), or about 80.11 inches.


• Divide the distance traveled by the tire circumference to find the number of revolutions made. First, convert 100 feet to 1200 inches.

TIRE A: 100 ft.76.03 in.

1200 in.76.03 in.= 100 ft.

80.11 in.1200 in.

80.11 in.=

15.8 revolutions

TIRE B:

15.0 revolutions


Ex. 5: Finding Arc Length• Track. The track shown has six lanes. Each

lane is 1.25 meters wide. There is 180° arc at the end of each track. The radii for the arcs in the first two lanes are given.

a. Find the distance around Lane 1.b. Find the distance around Lane 2.

Ex. 5: Finding Arc Lengtha. Find the distance around Lane 1. The track is made up of two semicircles and two

straight sections with length s. To find the total distance around each lane, find the sum of the lengths of each part. Round decimal answers to one decimal place.

• Distance = 2s + 2r1

= 2(108.9) + 2(29.00) 400.0 meters

• Distance = 2s + 2r2

= 2(108.9) + 2(30.25) 407.9 meters

Ex. 5: Lane 1

Ex. 5: Lane 2

geometry b bellwork

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