# Circumference

Using only this photo could you find the circumference of this carousel to within a few feet?

First we could take the height of a person who looks to be around 6 feet and figure out the radius of the circle:

5 * 6 = roughly 30 feet

With the radius we can use **π** to determine the **circumference** directly.:

**π = circumference / diameter**

**circumference = 2 **x **π **x** r**

**circumference = 2 **x** 3.14 **x** 30**

**circumference = 188 feet **

We correctly find that it’s approximately 188 feet around the perimeter of the wheel, all thanks to π!

# Area

How can we estimate area of any circle given its radius?

Let’s approximate the answer using a pizza slice analogy. **Below is an interactive illustration, **click the arrows to change the number of slices in the pie:

As we increase n, the perimeter of the pizza approaches the circumference of the circle. As we increase the number of slices:

- the height of the slice approaches the radius of the circle (
**h = r**) - the area of the pizza approaches the area of the circle (
**area of pizza = area of circle**)

This leads to a well known equation which relates the area and radius (or circumference) of any circle:

### area of circle = π x r^2