Annulus
Pronunciation: /ˈæn.jə.ləs/ Explain
|
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.
Click here for the answer. Answer: The formula for the area of an annulus is
A = π(r12 - r22),
r1 > r2. Plugging in
3m for r1
and
1m for r2,
we get A = π(32-12)
= π(9-1) = π·8 ≈ 25.13.
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Examples of Annulus
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Understanding Check
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
- 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
- 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
More Information
- Annulus. www.mathisfun.com. Math Is Fun. 6/19/2018. https://www.mathsisfun.com/geometry/annulus.html.
Cite this article as:
McAdams, David E. Annulus. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/annulus.html.Image Credits
- All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
- Paper Towel Roll: Santeri Viinamäki, commons.wikimedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license. https://commons.wikimedia.org/wiki/File:Paper_towel.jpg.
- Tape Roll: BenFrantzDale, commons.wikimedia.org. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. https://commons.wikimedia.org/wiki/File:Transparent_duct_tape_roll.png.
- Pipe Shape: Fito, commons.wikimedia.org. This file is released to public domain by the artist. https://commons.wikimedia.org/wiki/File:Pipe_shape.png.
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.)
6/14/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
12/27/2009: Added "Reference" and "More Information". (McAdams, David E.)
12/19/2008: Changed figure 1 to a manipulative. (McAdams, David E.)
6/23/2008: Reorganized content, added challenge and understanding check. (McAdams, David E.)
4/18/2008: Added illustrations. (McAdams, David E.)
4/17/2008: Initial version. (McAdams, David E.)
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