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232 lines
9.0 KiB
HTML
232 lines
9.0 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/sphere.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:49 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Sphere</title>
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<script language="JavaScript" type="text/javascript">reSpell=[["center","centre"]];</script>
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<style>
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.box { display: inline-block; vertical-align: top; margin: 10px;}
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</style>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<link rel="preload" href="../style4.css" as="style">
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<link rel="preload" href="../main4.js" as="script">
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<link rel="stylesheet" href="../style4.css">
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</script>
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</head>
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="search" role="search"></div>
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<div id="linkto"></div>
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<div id="menuSlim" class="menu"></div>
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<div id="menuTiny" class="menu"></div>
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</nav>
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<div id="extra"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Sphere</h1>
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<p class="center"><i>Go to <a href="#Area">Surface Area</a> or <a href="#Volume">Volume</a>.</i></p>
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<div class="flexx">
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<div class="col def" style=" text-align:left; margin:0; width:240px;">
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<h3>Sphere Facts</h3>
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<p><b>Notice these interesting things:</b></p>
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<p class="center"><img src="images/sphere-radius.svg" alt="Sphere Radius" height="180" width="180"></p>
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<ul>
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<li>It is perfectly symmetrical</li>
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<li>All points on the surface
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are the<br>
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same distance
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<b>"r"</b> from the center</li>
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<li>It has <b>no</b> edges or<br>
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vertices (corners)</li>
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<li>It has one <b>surface</b><br>
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(not a "face" as it isn't flat)</li>
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<li>It is <b>not</b> a <a href="polyhedron.html">polyhedron</a></li>
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</ul>
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</div>
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<div class="col">
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<img src="images/sphere-glass.jpg" alt="Glass Sphere" height="299" width="304"><br>
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<i>Glass Sphere</i>.<br>
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Balls and marbles are shaped like spheres.
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</div>
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</div>
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<p>
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You can spin or drag this sphere:
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</p>
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<div class="script" style="height: 460px;">
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images/poly-gl.js?mode=sphere
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</div>
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<div style="float:right; margin: 0 0 5px 10px; width:260px;">
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<div class="script" style="height: 250px;">
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images/balloon.js
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</div>
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</div>
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<h2>Largest Volume for Smallest Surface</h2>
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<p>Of all the shapes, a sphere has the smallest surface area for a volume. Or put another way it can contain the greatest volume for a fixed surface area.</p>
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<p>Example: if you blow up a balloon it naturally forms a sphere because it is trying to hold as much air as possible with as small a surface as possible. Press the Play button to see.</p>
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<p> </p>
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<div style="clear:both"></div>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/bubble.jpg" alt="bubble" height="193" width="200"></p>
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<h2>In Nature</h2>
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<p>The sphere appears in nature when a surface wants to be as small as possible. Examples include bubbles and water drops. Can you think of more?</p>
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<p><br></p>
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<h2>Volume and Surface Area</h2>
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<a id="Area"></a>
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<p class="center"><img src="images/sphere-radius.svg" alt="Sphere Radius" height="180" width="180"></p>
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<p class="center larger">Surface Area = 4 × <span class="times">π</span> × r<sup>2</sup></p>
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<div class="example">
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<h3>Example: r = 5</h3>
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<div class="tbl">
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<div class="row"><span class="left"><span class="center">Surface Area </span></span><span class="right">= 4 × <span class="times">π</span> × r<sup>2</sup></span></div>
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<div class="row"><span class="left"> </span><span class="right">= 4 × <span class="times">π</span> × 5<sup>2</sup></span></div>
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<div class="row"><span class="left"> </span><span class="right">= 4 × <span class="times">π</span> × 25</span></div>
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<div class="row"><span class="left"> </span><span class="right">= 100 <span class="times">π</span></span></div>
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<div class="row"><span class="left"> </span><span class="right">≈ 314</span></div>
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</div>
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</div>
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<a id="Volume"></a><p> </p>
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<p class="center larger">Volume = (4/3) × <span class="times">π</span> × r<sup>3</sup></p>
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<div class="example">
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<h3>Example: r = 5</h3>
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<div class="tbl">
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<div class="row"><span class="left">Volume</span><span class="right"> = (4/3) × <span class="times">π</span> × r<sup>3</sup></span></div>
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<div class="row"><span class="left"> </span><span class="right"> = (4/3) × <span class="times">π</span> × 5<sup>3</sup></span></div>
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<div class="row"><span class="left"> </span><span class="right">= (4/3) × <span class="times">π</span> × 125</span></div>
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<div class="row"><span class="left"> </span><span class="right">≈ 524</span></div>
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</div>
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</div>
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<p>Try dragging point "A":</p>
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<iframe src="isphere.html" scrolling="no" style="display:block; width:362px; height:302px; background-color:white; overflow:hidden; margin:auto; border: none;"></iframe>
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<p>Also see <a href="sphere-volume-area.html">Volume and Area of a Sphere Calculator</a></p>
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<p> </p>
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<h2><span itemprop="name">Spheroid</span></h2>
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<table width="100%" border="0">
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<tbody>
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<tr>
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<td align="right" width="40%">
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<h3>The Earth</h3>
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<p>The Planet Earth, our home, is <i>nearly</i> a sphere, except that it is squashed a little at the poles.</p></td>
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<td><img src="images/planet-earth.jpg" alt="Earth is a Spheroid" height="162" width="162"></td>
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<td align="left" width="40%"><br>
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So it is technically a <a href="spheroid.html">spheroid</a>, but a very mild version of one.</td>
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</tr>
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<tr>
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<td colspan="3" align="center">
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<p>Here is a more extreme spheroid:</p>
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<p class="center"><img src="images/spheroid.svg" alt="Spheroid" height="175" width="306"></p></td>
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</tr>
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</tbody></table>
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<p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/hemisphere.jpg" alt="sphere crystal" height="287" width="221"></p>
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<h2>Hemisphere</h2>
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<p>A <b>hemisphere</b> is an exact half of a sphere.</p>
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<div style="clear:both"></div>
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<h2>Other Cool Spheres</h2>
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<p class="center"><img src="images/sphere-crystal.jpg" alt="sphere crystal" height="250" width="301"></p>
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<p class="center"><img src="images/marble.jpg" alt="marble" height="192" width="190"></p>
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<table align="center" cellspacing="5" border="0">
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<tbody>
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<tr>
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<td><img src="images/sphere-jade.jpg" alt="Jade Sphere" height="178" width="173"></td>
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<td><img src="images/sphere-check.jpg" alt="Light Sphere" height="178" width="171"></td>
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</tr>
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<tr>
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<td><img src="images/sphere-dark.jpg" alt="Dark Sphere" height="178" width="166"></td>
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<td><img src="images/sphere-brass.jpg" alt="Brass Sphere" height="178" width="171"></td>
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</tr>
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</tbody></table>
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<p> </p>
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<div class="questions">865,866,867,868, 1831, 1832, 3383, 3384, 3385, 3386</div>
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<div class="related">
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<a href="sphere-volume-area.html">Volume and Area of a Sphere Calculator</a>
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<a href="torus.html">Torus</a>
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<a href="cylinder.html">Cylinder</a>
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<a href="cone.html">Cone</a>
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<a href="cone-sphere-cylinder.html">Cone vs Sphere vs Cylinder</a>
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<a href="prisms.html">Prisms</a>
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<a href="polyhedron.html">Polyhedron</a>
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<a href="../platonic_solids.html">Platonic Solids</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<div id="adend" class="centerfull noprint"></div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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</div>
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</body><!-- #EndTemplate -->
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<!-- Mirrored from www.mathsisfun.com/geometry/sphere.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:52 GMT -->
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