# 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:

`\large{\pi} = \dfrac{\text{circumference}}{\text{diameter}}`

`\large{\pi} = \dfrac{\text{circumference}}{2 \times r}`

`\text{circumference} = 2 \times \pi \times r`

`\text{circumference} \approx 2 \times 3.14 \times 30`

`\text{circumference} \approx 188 \text{ 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 the 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 of any circle:

`\text{area of circle} = \pi r^2`