﻿ Circumference of a circle explained with examples, pictures and an interactive HTML5 Applet. The circumference is just...

# 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.

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

$$Circumference = \pi \cdot diameter$$

$$Circumference = 2\pi\cdot radius$$
**These two formulas are just two different ways of finding the same thing (circumference) because the diameter of a circle $$=2 \cdot radius$$. 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 ($$\pi \cdot diameter$$)

### The Circle Song

The rotating line on the is an example of a circle's radius.

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

### Practice Problems

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

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

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

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

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}

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 }}

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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