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100 lines
4.8 KiB
HTML
100 lines
4.8 KiB
HTML
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<title>Why is a Pyramid like a Cone?</title>
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<h1 class="center">Why is a Pyramid like a Cone?</h1>
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<p>Try increasing the number of sides:</p>
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<script type="text/javascript">geomoblique3dMain("pyrn");</script>
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<p>Yes! The <a href="pyramids.html">pyramid</a> starts to look like a <a href="cone.html">cone</a>!</p>
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<p>Also try moving points A and B.</p>
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<h2>Volume</h2>
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<p>The volume formulas are the same:</p>
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<p class="center larger">V = <span class="intbl"><em>1</em><strong>3</strong></span> × (Base Area) × Height</p>
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<p>For a circular cone the base area is <span class="times">π</span>r<sup>2</sup> (where r is radius) so we get:</p>
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<p class="center larger">Volume of Circular Cone = <span class="intbl"><em>1</em><strong>3</strong></span> × (<span class="times">π</span>r<sup>2</sup>) × Height</p>
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<p>For a square pyramid the base area is s<sup>2</sup> (where s is side length) so we get:</p>
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<p class="center larger">Volume of Square Pyramid = <span class="intbl"><em>1</em><strong>3</strong></span> × (s<sup>2</sup>) × Height</p>
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<p>For other pyramids we just have to work out the base area.</p>
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<h2>Right vs Oblique</h2>
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<p>And it doesn't matter if it is <b>right</b> (top directly above base) or <b>oblique</b> (slanted), the volume formula still works, but remember:</p>
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<p class="center large">The height is at right angles to the base!</p>
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<p class="center"><img src="images/cone-oblique.svg" alt="oblique cone" /></p>
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<div class="related">
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<a href="pyramids.html">Pyramid</a>
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<a href="cone-sphere-cylinder.html">Cone vs Sphere vs Cylinder</a>
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<a href="cone.html">Cone</a>
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<a href="index.html">Geometry Index</a>
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