6.5 The Circumference/Diameter Ratio
ACTIVITY
- Work with a partner and find the ratio using the values in the table and answer
the question below.
OBJECT
CIRCUMFERENCE
(C)
DIAMETER (d)
Plate
82 cm
26 cm
Mug
5.18 cm
1.65 cm
Wheel
40.5 cm
12.95 cm
Clock
68.2 cm
21.7 cm
Coaster
30.6 cm
9.8 cm
𝐶
RATIO 𝑑
How do the circumference and diameter appear to be related?
___________________________ - The distance around a circle.
Circumference Conjecture
If C is the circumference and d is the diameter of a circle, then there is a number π such that
C = ___________. If d = 2r where r is the radius, then C = ___________.
LESSON 6.5 THE CIRCUMFERENCE/DIAMETER RATIO
1
Example 1: Find the exact circumference of each circle then use π = 3.14 to approximate
your answers to the nearest tenth.
a.
b.
4.5 m
24 m
c.
d.
6.78 m
LESSON 6.5 THE CIRCUMFERENCE/DIAMETER RATIO
13 m
2
Example 2: Find the radius and diameter of the circle with each given circumference.
a. C ≈ 22.75π cm
c. C ≈ 172.7 yd
b. C ≈ 208.81 m
d. C ≈ 25π in
Example 3: Read the following problems, solve for the circumference when given the
diameter or radius.
a) Brett refills the oil in his car using a funnel. The upper rim of the funnel has a diameter
of 6 inches. Approximate the circumference of the funnel.
LESSON 6.5 THE CIRCUMFERENCE/DIAMETER RATIO
3
b) The radius of a merry-go-round is 19 cm. Approximately how far does the horse on
the edge travel in one revolution?
c) If the distance from the center of a Ferris wheel to one of the seats is 65 ft, what is the
distance traveled by a seated person, to the nearest foot, in one revolution?
d) The students in Ms. Hall’s 4th grade class sit in a circle for story time. The circle they
form has a diameter of 9 yards. Approximate the circumference of the circle.
LESSON 6.5 THE CIRCUMFERENCE/DIAMETER RATIO
4
Example 4: Read the following problems, and solve for how far the person is running.
a) Beth ran 8 times around a circular track that has a radius of 24 meters. To the nearest
tenth of a meter, how far did Beth run?
b) Robert ran 6 times around a circular track that has a diameter of 43 meters. To the
nearest tenth of a meter, how far did Robert run?
Example 5: Using the information provided in the problem, solve for what is missing.
a) The distance around the equator of Earth is about 25,376 kilometers. To the nearest
kilometer, what is the equatorial diameter of Earth?
LESSON 6.5 THE CIRCUMFERENCE/DIAMETER RATIO
5
b) The distance around a basketball is 765 meters. To the nearest meter, what is the
diameter of the basketball?
REVIEW
1) What does it mean when you are asked to find the EXACT value
of the circumference?
2) What are the two equations for finding circumference?
a. ____________________
b. ____________________
HOMEWORK: PP. 333-334 # 1 – 11; 19
LESSON 6.5 THE CIRCUMFERENCE/DIAMETER RATIO
6