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114 lines
5.6 KiB
HTML
114 lines
5.6 KiB
HTML
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<!-- Mirrored from www.mathsisfun.com/geometry/annulus.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:42:55 GMT -->
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<head>
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<title>Annulus</title>
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<a href="../about-ads.html">About Ads</a></div>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 class="center">Annulus </h1>
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<table border="0" align="center">
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<tr>
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<td><img src="images/annulus.svg" alt="annulus r and R" /></td>
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<td> </td>
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<td><p>An annulus is a flat shape like a ring.<br />
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<br />
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Its edges are two <a href="circle.html">circles</a> that have the same center.</p>
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<p> </p></td>
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</tr>
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</table>
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<p class="center"><img src="images/washers.jpg" width="300" height="117" alt="Washers (various)"><br>
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The face of a metal washer is an annulus</p>
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<div class="words">
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<p>Something shaped like an annulus is said to be <b>annular</b>.</p>
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<p>Saturn has annular rings:</p>
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<p class="center"><img src="../images/saturn-far-side.jpg" width="250" height="123" alt="saturn"></p>
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</div>
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<h2>Area</h2>
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<p>Because it is <b>a circle with a circular hole</b>, you can calculate the <a href="circle-area.html">area</a> by subtracting the area of the "hole" from the big circle's area:</p>
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<p class="center"><img src="images/annulus-area.svg" alt="annulus area pi R^2 - pi r^2" /></p>
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<p class="center larger">Area = <span class="times">π</span>R<sup>2</sup> − <span class="times">π</span>r<sup>2</sup> <br />
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= <span class="times">π</span>( R<sup>2</sup> − r<sup>2 </sup>)</p>
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<p> </p>
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<div class="example">
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<p><img style="float:right; margin: 10px;" src="images/annulus-pipe.jpg" width="118" height="184" alt="annulus pipe" /></p>
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<h3>Example: a steel pipe has an outside diameter (OD) of 100mm and an inside diameter (ID) of 80mm, what is the area of the cross section?</h3>
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<p>Convert diameter to radius for both outside and inside circles:</p>
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<ul>
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<li>R = 100 mm / 2 = 50 mm</li>
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<li>r = 80 mm / 2 = 40 mm</li>
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</ul>
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<p>Now calculate area:</p>
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<div class="so">Area =<span class="times"> π</span>( R<sup>2</sup> - r<sup>2 </sup>)</div>
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<div class="so"> Area = 3.14159... × ( 50<sup>2</sup> − 40<sup>2 </sup>) </div>
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<div class="so"> Area = 3.14159... × (2500 − 1600)</div>
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<div class="so"> Area = 3.14159... × 900</div>
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<div class="so"> Area = 2827 mm<sup>2</sup> (to nearest mm<sup>2</sup>) </div>
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</div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(3234, 9054, 9055, 9056, 9057, 9058, 9059, 9060, 9061, 224);</script> </div>
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<div class="related"> <a href="circle.html">Circle</a> <a href="circle-area.html">Area of Circle</a> <a href="index.html">Geometry Index</a> </div>
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Copyright © 2018 MathsIsFun.com
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