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Clare wonders if the height of the toilet paper tube or the distance around the tube is greater. What information would she need in order to solve the problem? How could she find this out?
Your teacher will give you two circular objects.
Measure the diameter and the circumference of each circle to the nearest tenth of a centimeter. Record your measurements in the first two rows of the table.
| object | diameter (cm) | circumference (cm) |
|---|---|---|
Plot your diameter and circumference values on the coordinate plane. What do you notice?
Find out the measurements from another group that measured different objects. Record their values in your table and plot them on your same coordinate plane.
What do you notice about the diameter and circumference values for these four circles?
Here are five circles. One measurement for each circle is given in the table.
Use the constant of proportionality estimated in the previous activity to complete the table.
| diameter (cm) | circumference (cm) | |
|---|---|---|
| circle A | 3 | |
| circle B | 10 | |
| circle C | 24 | |
| circle D | 18 | |
| circle E | 1 |
There is a proportional relationship between the diameter and circumference of any circle. That means that if we write
The exact value for the constant of proportionality is called pi, and its symbol is
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
The relationship between the circumference and the diameter can be written as
There is a proportional relationship between the diameter and circumference of any circle. The constant of proportionality is pi. The symbol for pi is
This relationship can be represented with the equation
Some approximations for
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