6.4 Day 1 – Circumference of a Circle
Essential question: How do you find the circumference of a circle?
Warm-up:
Remember that a circle is a set of points in a plane that are a fixed distance from the center.
Label the center, radius, diameter and the circumference of the circle.
Example 1 – Exploring the Relationship between Circumference and Diameter
A) Use a measuring tape to find the circumference of five circular objects. Then measure
the distance across each item to find its diameter. Record the measurements of each object
in the table below.
B) Divide the circumference of each object by its diameter. Round your answer to the
nearest hundredth.
Object
Circumference Diameter
C
d
C
d
C) Describe what you notice about the ratio C in your table.
d
D) Compare your results with other students. Make a conjecture about the relationship
between the circumference and the diameter of a circle.
E) How could you estimate the circumference of a circular object without measuring it if you
know the diameter?
F) Fill in the blanks: The ratio of __________________________ to _______________________ in a
circle is ____, which is approximated by using ________________.
Example 2 – Finding the Circumference of a Circle
There are two formulas for circumference of a circle:
C = 2πr
or
C= πd
Why are there two formulas? When would you use each?
Find the circumference of the circle to the nearest hundredth. Use 3.14 for π.
5cm
Which formula should you use?
Use the formula to find the circumference.
A) After calculating the circumference of a circle, how do you know your answer is
reasonable?
Example 3 – Using Circumference
The circumference of a circular pool is 47 feet. A model boat is moving directly across the
pool, along the diameter, at a rate of 2 feet per second. How long does it take the boat to
get to the other side?
A) Draw a diagram of the problem.
B) What formula would you use? Why?
C) Use the formula to find your answer.
D) Answer the question in a complete sentence.
You Try It!
1) How long would it take the boat to get across the pond if the model boat traveled at a
rate of 2.5 feet per second?
2) The circumference of a circular garden is 42 meters. A gardener is using a machine to dig
a straight line along the diameter of the garden at a rate of 10 meters per hour. How many
hours will it take the gardener to dig across the garden?
PRACTICE
Find the circumference of each circle to the nearest tenth, if necessary. Use 3.14 for π.
USE THE FORMULA!
1) diameter = 6 cm
2) radius = 5.5 mm
3) diameter = 7.2 feet
Find each missing measurement to the nearest hundredth. Use 3.14 for π.
4) r = 8 m; d = ______, C ≈ ______
5) r = _____; d = 9.6 cm, C ≈ ______
6) r = _______; d = ______, C ≈ 84.9 ft.
7) r = _______; d = ______, C ≈ π
8) A tire has a circumference of 62.8 inches. What is the diameter of the tire? Use 3.14 for
π.
9) Colleen walks a circular track with a radius of 71 yards. Use 3.14 for π.
A) How far does she walk in 5 laps?
B) If she walks at a rate of 4 miles per hour, how long, in hours, will it take her to do her laps?
Hint: 1,760 yards = 1 mile
10) Shelly wants to put ribbon around the top and bottom of a circular can she is
decorating. The diameter of the can is 11 inches. Use 3.14 for π.
A) Shelly can only buy the ribbon in a whole number of inches. How much total ribbon must
she buy?
B) How much will she have to cut off?
11) Error analysis. Lori says the radius of the circle is 20 feet. What is Lori’s error? Find the
correct radius of the circle.
x ft.
C = 62.8 ft.