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

## Want to join the conversation?

• How do you find area when all you have is circumference (60cm)?
• Divide by pi to get the diameter, then divide that by two to get the radius, then solve the formula for the area of a circle. pi r squared.
• I understand pi x r squared, I understand how pi x r x r will get you the area, but the interactive illustration above shows area as 1/2 x circumference, and I'm not seeing that in the model. Can someone please explain?
• It's not showing area as 1/2 * circumference. It is showing area = base * height. The base is 1/2 * circumference or πr. The height is r. So, area = πr².
• Is there any other formulas for circle or ellipse?
• what is the number of pi?
• What is circumference relative to perimeter?
(1 vote)
• Perimeter = the distance around the outside (The definition my 3rd grade teacher gave) The circumference is the distance around the outside of a circle.