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# Circumference of a Circle

## What is circumference anyway?

Answer: The circumference of a circle is the edge or rim of a circle itself. It is the equivalent of 'perimeter' for a circle. In other words, if you took a circle and unrolled it, you would have its circumference. You can use either of the formulas below to find the circumference . One formula use the radius of a circle; the other formula uses the diameter.

## What is the formula for circumference?

 Formula using Diameter Formula using Radius $$Circumference = \pi \cdot diameter$$ $$Circumference = 2\pi\cdot radius$$
**These two formulas are just two different ways of finding the same thing (circumference) because the diameter of a circle =2• radius. So you can use whichever formula is more convenient. If you know a circle's radius, use the first version of the formula; if you know the diameter, use the second.
The Circle Song
The rotating line on the left is an example of a circle's radius.

If the radius of a circle is 1 inch (1"), then the circumference of the circle = 2Π• 1" ≈   6.28"

## Interactive Circumference of a Circle Applet

 Formula Radius Diameter Color of Circumference Blue Black Red Yellow
$$Circumference= 2 \cdot \pi \cdot radius$$


Practice Problems

Problem 1) What is the circumference of the circle below. (Round your answer to the nearest inch.)

 Circumference

Problem 2) What is the circle's circumference? (Round to nearest tenth of an inch)
 Circumference

Problem 3) What is the circumference of the circle pictured below? (Round your answer to the nearest inch.)
 Circumference

Problem 4) What is the circumference of the circle pictured below? (Round your answer to the nearest tenth of an inch.)
 Circumference

Challenge Problems
Problem 5) What is the circumference of a circle with a radius of 5"?
 Circumference

Problem 6) A circle's circumference is $$22\pi \text{ inches}$$. What is the radius of this circle?