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Area of an Annulus - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

An annulus is similar to a ring or a castle's moat; it is the area between two concentric circles. Calculating the annulus area, therefore, involves finding the difference of the two circles' area. A common trick on annulus problems is to give the distance between the small and large circle, and not the large circle's radius. Related topics include area of a sector, area of a circle and area of an segment.

To find the area of an annulus where an annulus is the region between 2 circles. We have to think about this in terms of 2 different circles, one being the larger outer circle and one being the smaller inner circle. The area of this region in between them is going to equal so I can say the area of the annulus is equal to the area of the large circle subtracted by the area of the smaller circle. So if we go back to our original drawing, we see that we have 2 arcs. A little r for the smaller circle and a capital R for the larger circle, so the area of the annulus will be pi times big R squared so that will give you the area of the whole circle and we're going to take out the middle part. So that will be subtracted by pi times the little r squared. So when you're trying to calculate the area of an annulus you need to know the radius one for the larger circle and one for the smaller circle and subtract the areas.

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