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Measuring the Universe

# 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 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: