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Learning Targets
- I can choose an approximation for π based on the situation or problem.
- If I know the radius, diameter, or circumference of a circle, I can find the other two.
Notes
Notes
The circumference of a circle, C, is π times the diameter, d. The diameter is twice the radius, r. So if we know any one of these measurements for a particular circle, we can find the others. We can write the relationships between these different measures using equations:
d = 2 r
C = π d
C = 2 π r
If the diameter of a car tire is 60 cm, that means the radius is 30 cm and the circumference is 60 ⋅ π or about 188 cm.
If the radius of a clock is 5 in, that means the diameter is 10 in, and the circumference is 10 ⋅ π or about 31 in.
If a ring has a circumference of 44 mm, that means the diameter is 44 ÷ π, which is about 14 mm, and the radius is about 7 mm.
Activities
Activities
4.1 What Do We Know? What Can We Estimate?
4.1 What Do We Know? What Can We Estimate?
Here are some pictures of circular objects, with measurement tools shown. The measurement tool on each picture reads as follows:
- Wagon wheel: 3 feet
- Plane propeller: 24 inches
- Sliced Orange: 20 centimeters
- For each picture, which measurement is shown?
- Based on this information, what measurement(s) could you estimate for each picture?
4.2 Using Pi (π)
4.2 Using Pi (π)
In the previous activity, we looked at pictures of circular objects. One measurement for each object is listed in the table.
Use 3.14 as π in this activity.
- Complete the table.
- A bug was sitting on the tip of a wind turbine blade that was 24 inches long when it started to rotate. The bug held on for 5 rotations before flying away. How far did the bug travel before it flew off?
- If you choose to, you can change the settings in the applet and enter your calculation in the box at the bottom to check your work.
- Just for fun, use the slider marked “turn,” and the other one that will appear, to watch the bug’s motion.
The proportional relationship between diameter and circumference of a circle can be applied in more complex situations that require multi-step solutions.
Because the diameter is twice the radius, we can write the relationship between the circumference of a circle and its radius like this: C = 2𝛑r.
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