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## 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, equals, start fraction, start text, c, i, r, c, u, m, f, e, r, e, n, c, e, end text, divided by, start text, d, i, a, m, e, t, e, r, end text, end fraction
pi, equals, start fraction, start text, c, i, r, c, u, m, f, e, r, e, n, c, e, end text, divided by, 2, times, r, end fraction
start text, c, i, r, c, u, m, f, e, r, e, n, c, e, end text, equals, 2, times, pi, times, r
start text, c, i, r, c, u, m, f, e, r, e, n, c, e, end text, approximately equals, 2, times, 3, point, 14, times, 30
start text, c, i, r, c, u, m, f, e, r, e, n, c, e, end text, approximately equals, 188, start text, space, f, e, e, t, end text

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:
start text, a, r, e, a, space, o, f, space, c, i, r, c, l, e, end text, equals, pi, r, squared

## 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.
• what is the number of pi?
• Is there any other formulas for circle or ellipse?
• 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.