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What is an Annulus in Math? - Definition & Formula

Instructor: Allison Petrovic

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

Have you ever heard of an annulus? If you have ever eaten a doughnut, you have seen an annulus! In this lesson, we will learn the definition and discover how to find the area of an annulus!

Glazed Doughnuts!

Think about the last time you had a glazed doughnut. Yummy! If your teacher asked you the shape of your glazed doughnut, what would you say? You may be thinking, Well when I look at it from above, it is in the shape of a circle! But let's think about this. Circles do not have holes in the middle of them. So what type of shape would your doughnut be? What is the shape that looks like a circle but has a hole in the middle of it? The shape is called an annulus!

What is an Annulus?

An annulus is basically a ring--a circle with a circular hole in the middle. Have you ever seen a washer? Not the kind that you use to wash your clothes, but the kind of washer that is used with nuts and bolts. Ask a parent to dig one out of the tool box! A washer is a great example of what an annulus looks like--just like a ring.


Washers are annuli (the plural word for annulus).
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Area of an Annulus

Let's figure out how to calculate the area of an annulus! In the picture below, the annulus is blue. Do you see how the annulus looks like it has two circles? It looks like there is one big blue circle (this larger, outer circle is the ring) and one small yellow circle, which is the hole. The area of the annulus is equal to the area of the big blue circle minus the area of the small yellow circle.


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So, to find the area of an annulus, we must find the area of the big blue circle and then subtract the area of the small yellow circle. Keep in mind that the formula for the area of a circle is pi times the radius (r) squared (or, pi x r^2)


Formula for the area of an annulus
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