Embedded Files
Learning Targets
- I can describe the relationship between circumference and diameter of any circle.
- I can explain what π means.
Notes
Notes
There is a proportional relationship between the diameter and circumference of any circle. That means that if we write C for circumference and d for diameter, we know that C = k d, where k is the constant of proportionality.
The exact value for the constant of proportionality is called π. Some frequently used approximations for π are (22/7), 3.14, and 3.14159, but none of these is exactly π because π goes on forever.
We can use this to estimate the circumference if we know the diameter, and vice versa. For example, using 3.1 as an approximation for π, if a circle has a diameter of 4 cm, then the circumference is about (3.1) ⋅ 4 = 12.4 or 12.4 cm.
The relationship between the circumference and the diameter can be written as
C = π d
For fun...check out this animation.
Open the website to see the first one million digits of pi (π).
Vocabulary
Vocabulary
pi (π): The Greek letter π (pronounced "pie") stands for the number that is the constant of proportionality between the circumference of a circle and its diameter. If d is the diameter and C is the circumference, then C = π d.
Activities
Activities
3.2 Measuring Circumference and Diameter
3.2 Measuring Circumference and Diameter
Coins, cookies, and drinking glasses are some examples of common circular objects.
USE THE FOLLOWING DIAMETERS:
6 UNITS
10 UNITS
14 UNITS
- Explore the applet to find the circumference of three circular objects to the nearest tenth of a unit. Record your measurements in a table.
- Using the graphing applet, plot the diameter and circumference values from the table on the coordinate plane. What do you notice?
Plot the points from two other groups on the same coordinate plane. Do you see the same pattern that you noticed earlier?
Things to Note
Things to Note
- This is a proportional relationship. The graph goes through (0, 0) and the constant of proportionality is pi (π).
- To get an idea of the constant of proportionality…use your values in your table and take circumference ÷ diameter.
- The quotients will not be EXACTLY the same due to the fact that we used values that were rounded to the nearest tenth of a unit.
3.3 Calculating Circumference and Diameter
3.3 Calculating Circumference and Diameter
Here are five circles. One measurement for each circle is given in the table.
- Use the constant of proportionality estimated in the previous activity (π) to complete the table.
Things to Highlight
Things to Highlight
- Diameter and circumference are proportional to each other!
- We know Circumference = 3.14 • d …
- So if we know the circumference or diameter, we can find the other!
- We can approximate 𝛑 using 22/7, 3.14, or 3.14159. None of these are exactly Pi because Pi goes on forever!
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