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## NASA

### Course: NASA>Unit 2

Lesson 3: Orbital mechanics

# Applying pi

## Circumference

Using only this photo, could you find the circumference of this ferris wheel 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:

$\pi =\frac{\text{circumference}}{\text{diameter}}$
$\pi =\frac{\text{circumference}}{2×r}$
$\text{circumference}=2×\pi ×r$
$\text{circumference}\approx 2×3.14×30$

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