The circumference of a circle is the distance around it. There are two primary formulas to calculate the circumference: $C = \pi d$ and $C = 2\pi r$. The first formula uses the diameter ($d$) of the circle, which is the distance across the circle through the center. The second formula uses the radius ($r$) of the circle, which is the distance from the center to any point on the circle. Since the diameter is twice the radius ($d = 2r$), both formulas are essentially the same, just expressed in terms of different measurements.
In these formulas, $\pi$ (pi) is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter. Understanding these formulas allows you to calculate the circumference of any circle if you know either its diameter or its radius. Let's practice!
Match the following terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Circumference | A. Distance from the center of the circle to any point on the circle. |
| 2. Diameter | B. The ratio of a circle's circumference to its diameter, approximately 3.14159. |
| 3. Radius | C. The distance around the circle. |
| 4. $\pi$ (Pi) | D. Distance across the circle through the center. |
Complete the following paragraph with the correct words:
The _______ of a circle can be found using two formulas: $C = \pi d$ and $C = 2 \pi r$. In these formulas, '$d$' represents the _______, which is twice the length of the _______. The symbol $\pi$ represents a _______, approximately equal to 3.14159.
Explain in your own words why knowing either the radius or diameter of a circle is enough to calculate its circumference. Give a real-world example of when you might need to calculate the circumference of a circular object.
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