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Circumference of a Circle

Formula for circumference with examples

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?

Answer:
Formula using Diameter Formula using Radius
$$Circumference = \pi \cdot diameter$$ $$ Circumference = 2\pi\cdot radius $$
circumference formula picture
**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

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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"
applet

Interactive Circumference of a Circle Applet

(Applet in own window)
Formula
Color of Circumference
$$ Circumference= 2 \cdot \pi \cdot radius $$
$$ $$



Practice Problems

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


Problem 2) What is the circle's circumference? (Round to nearest tenth of an inch)
circumference of 9 inch circle
Circumference

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

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

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?
Answer
Problem 7) A circle's circumference is 102". What is the diameter of the circle?
Diameter