Circumference and Area of a Circle

The **diameter** of a circle is the distance from one point on the circle to another point on the circle, through its center.

The **radius** of a circle is the distance from its center to a point on the circle.

The length of a circle's radius is half the length of its diameter.

The **circumference** of a circle is the distance around the circle.

**Pi** ($\text{\pi}$) is a non-repeating, non-terminating decimal which is equivalent to the ratio of a circle's circumference to its diameter. 3.14 is often used as an approximation of pi.

**Circumference = **$\pi $*d* or **2**$\pi $*r*

**Area = **$\text{\pi}$*r*^{2}

$\begin{array}{rcl}\text{Area}& =& \pi {r}^{2}\\ 100\pi {\text{cm}}^{2}& =& \pi {r}^{2}\\ 100\pi {\text{cm}}^{2}\xf7\pi & =& \pi {r}^{2}\xf7\pi \\ 100{\text{cm}}^{2}& =& {r}^{2}\\ \sqrt{100{\text{cm}}^{2}}& =& \sqrt{{r}^{2}}\\ 10\text{cm}& =& r\end{array}$

$\begin{array}{rcl}\text{Circumference}& =& 2\pi r\\ & =& 2\pi \text{(}10\text{cm)}\\ & =& 20\pi \text{cm}\end{array}$