Area of Annulus
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Theorem
Let $A$ be an annulus whose inner radius is $r$ and whose outer radius is $R$.
The area of $A$ is given by:
- $\map \Area A = \pi \paren {R^2 - r^2}$
Proof
The area of $A$ is seen to be:
From Area of Circle:
The result follows.
$\blacksquare$
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): annulus: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): annulus
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): annulus
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): annulus
- Weisstein, Eric W. "Annulus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Annulus.html