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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.

circumference colored
The glowing part in the circle above is the circumference.

Formula for 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.

Formula using Diameter

$$ Circumference = \pi \cdot diameter $$
circumference formula diameter picture

Formula using radius

$$ Circumference = 2\pi\cdot radius $$
circumference formula radius picture

**These two formulas are just two different ways of finding the same thing (circumference) because the diameter of a circle $$ =2 \cdot radius $$. So you can use whichever formula is more convenient. If you know a circle's radius, use the formula with radius ($$ 2 \cdot \pi \cdot radius $$) ; if you know the diameter, use the ($$ \pi \cdot diameter $$)

Interesting Fact about Circumference and Area

Practice Problems

Problem 1

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

circumference

$$ \eqalignno{ Circumference &= 2\pi\cdot radius \\ &= 2\pi\cdot 15 \\ &= \pi\cdot 30 \\ &=94} $$

Problem 2

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

circumference of 9 inch circle

$$ \eqalignno{ Circumference &= 2\pi\cdot radius \\ &=2\pi\cdot 9 \\ &=18\pi \\ &= 56.5} $$

Problem 3

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

circumference practice problem

$$ \eqalignno{ Circumference &= 2\pi\cdot radius \\ &=2\pi\cdot 71 \\ &=142\pi \\ &= 446} $$

Problem 4

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

circumference practice problem

Since they gave us the diameter in this picture, use the diameter version of the formula.

$$ \eqalignno{ Circumference &= \pi\cdot diameter \\ &= 13\pi \\ &= 40.8} $$

challenge problems

Challenge Problems

Problem 5

What is the circumference of a circle with a radius of 5"?

Since they gave us the radius in this problem, use the radius version of the formula.

$$ \eqalignno{ Circumference &= 2\pi\cdot radius \\ &=2\pi\cdot 5 \\ &=10\pi \\ &= 31.4} $$

Problem 6

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

Since the problem wants the radius, use the radius version of the formula.

$$ \eqalignno{ Circumference &= 2\pi\cdot radius \\ 22\pi &=2\pi\cdot r \\ \frac{22\pi}{\pi} &= \frac{2\pi\cdot r}{\pi} \\ 22 &= 2\cdot r \\ \frac{22}{2} &= r \\ r &= 11 \text{ inches }} $$

Problem 7

A circle's circumference is 102". What is the diameter of the circle?

Since the problem wants the radius, use the radius version of the formula.

$$ \eqalignno{ Circumference &= \pi\cdot diameter \\ 102 &= \pi\cdot diameter \\ \frac{102}{\pi} &= \frac{\pi\cdot diameter}{ \pi} \\ 32.5 &= diameter } $$


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