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120 lines
5.0 KiB
HTML
120 lines
5.0 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/geometry/pyramid-vs-cube.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:42 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<title>Pyramid vs Cube</title>
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<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents.">
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<style>
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.hide1 { color: #fff8dc; background-color: #fff8dc; border: 1px solid #ffd700; padding: 3px 15px 3px 15px; margin: 0 0 0 30px;}
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<div id="hdr"></div>
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<div id="cookOK"></div>
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</header>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Pyramid vs Cube</h1>
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<p>Make a pyramid that looks like this:</p>
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<p class="center"><img src="images/pyramid-side-3d.svg" alt="square pyramid" height="244" width="202"> <img src="images/pyramid-3-a.jpg" alt="square pyramid" height="239" width="209"></p>
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<ul>
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<li>It has a square base</li>
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<li>Its apex (top point) is directly above one corner</li>
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<li>Its height (the distance from that corner to the apex) is the same as the base length</li></ul>
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<p>You can print out this template to help you:</p>
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<div><a href="images/pyramid-side-net.png"><img src="images/pyramid-side-net.png" alt="Pyramid Net" style="max-width:300px; border: 1px solid blue;" height="573" width="916"></a></div>
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<p>Now make two more exactly the same, so we have three:</p>
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<p><img src="images/pyramid-3-b.jpg" alt="square pyramid three off" height="232" width="359"></p>
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<p>Fit them together and we get a cube:</p>
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<p><img src="images/pyramid-3-c.jpg" alt="square pyramid two joined" height="313" width="300"> <img src="images/pyramid-3-d.jpg" alt="square pyramid three joined" height="315" width="300"></p>
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<p>So <b>three</b> of those pyramids exactly make one cube!</p>
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<p>And so the volume of that <b>pyramid is exactly one third</b> of a cube.</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/pyramid-height-perimeter.svg" alt="Pyramid Perimeter and Height" height="186" width="278"></p>
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<p>We can extend that idea to come up with the volume of a general <a href="pyramids.html">pyramid</a>:</p>
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<p class="center large">Volume = <span class="intbl">
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<em>1</em>
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<strong>3</strong> </span> × [Base Area]× height</p>
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<div style="clear:both">
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</div>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/cone-dimensions.svg" alt="cone dimensions h=height, r=radius, s=side length" height="226" width="233"></p>
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<p>And, by thinking that a cone is just like a pyramid with a ridiculous number of sides, we can come up with the volume of a <a href="cone.html">cone</a>:</p>
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<p class="center large">Volume = <span class="intbl">
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<em>1</em>
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<strong>3</strong>
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</span> <span class="times"> π</span> × r<sup>2 </sup>× h</p>
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<p><br></p>
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<p>Isn't mathematics wonderful!</p>
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<p> </p>
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<div class="related">
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<a href="index.html">Geometry Index</a><a href="pyramid-vs-cone.html">Pyramid vs Cone</a><a href="prism-vs-cylinder.html">Prism vs Cylinder</a>
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</div>
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</article>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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