# Annulus

Pronunciation: /ˈæn.jə.ləs/ Explain

 Click on the blue points and drag them to change the figure. What is the difference between an annulus and a circle? Manipulative 1 - Annulus Created with GeoGebra.

An annulus is the region between two concentric circles.[2] The area of the annulus is the difference between the areas of the circles: A = π(r12 - r22) where r1 > r2.

#### Understanding Check

What is the area of an annulus with an inner radius of 1m and an outer radius of 3m?

### Examples of Annulus

 Figure 2: Roll of paper towels
 Figure 3: Roll of pipe tape
 Figure 4: Pipe. The cross section of a pipe is an annulus.

### Challenge

 1 A pipe has an inner radius of 3 cm. It has an outer radius of 3.5 cm. It is 100 cm long. What is the total volume of the pipe, not including the empty space inside? Click here for a hint. Hint: The volume of a cylinder is equal to the area of the base times the height of the cylinder (V = b·h). If the base is an annulus, what is the volume of the pipe? Click here for the answer. Answer: The volume of a pipe is the area of the base of the pipe times the height. The area of the base is A = π(r12 - r22), r1 > r2. So A = π((3.5 cm)2-(3 cm)2) ≈ 3.14159(12.25cm2 - 9cm2) ≈ 3.14159·3.25 cm2 ≈ 10.21 cm2. The volume of the pipe is equal to the area of the base times the height. V ≈ 10.21 cm2 · 100 cm V ≈ 1021 cm3. 2 The same pipe is made of a metal alloy with a density of 3g/cm3. What is the mass of the pipe in challenge 1? Click here for the answer. Answer: Using dimensional analysis, cm3·g/cm3 = gm. So multiplying the two quantities will give the correct result. 1021cm3·3gm/cm3 = 3063gm = 3.063kg.

### References

1. McAdams, David E.. All Math Words Dictionary, annulus. 2nd Classroom edition 20150108-4799968. pg 17. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pp 44-45. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 6/12/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/44/mode/1up/search/annulus. Buy the book

• Annulus. www.mathisfun.com. Math Is Fun. 6/19/2018. https://www.mathsisfun.com/geometry/annulus.html.

McAdams, David E. Annulus. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/annulus.html.

### Revision History

4/11/2019: Changed equations and expressions to new format. (McAdams, David E.)
1/12/2019: Replaced pipe image and paper towel image, and tape image. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)