e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
252 lines
10 KiB
HTML
252 lines
10 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
||
|
||
<!-- Mirrored from www.mathsisfun.com/geometry/cone.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:38 GMT -->
|
||
<head>
|
||
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
||
|
||
<!-- #BeginEditable "doctitle" -->
|
||
<title>Spinning Cone</title>
|
||
|
||
<script src="images/poly-gl.js" type="text/javascript"></script>
|
||
<link rel="stylesheet" type="text/css" href="../stylejs.css">
|
||
|
||
|
||
<!-- #EndEditable -->
|
||
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||
<meta name="HandheldFriendly" content="true">
|
||
<meta name="referrer" content="always">
|
||
<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
|
||
<link rel="preload" href="../style4.css" as="style">
|
||
<link rel="preload" href="../main4.js" as="script">
|
||
<link rel="stylesheet" href="../style4.css">
|
||
<script src="../main4.js" defer="defer"></script>
|
||
<!-- Global site tag (gtag.js) - Google Analytics -->
|
||
<script async="" src="https://www.googletagmanager.com/gtag/js?id=UA-29771508-1"></script>
|
||
<script>
|
||
window.dataLayer = window.dataLayer || [];
|
||
function gtag(){dataLayer.push(arguments);}
|
||
gtag('js', new Date());
|
||
gtag('config', 'UA-29771508-1');
|
||
</script>
|
||
</head>
|
||
|
||
<body id="bodybg">
|
||
|
||
<div id="stt"></div>
|
||
<div id="adTop"></div>
|
||
<header>
|
||
<div id="hdr"></div>
|
||
<div id="tran"></div>
|
||
<div id="adHide"></div>
|
||
<div id="cookOK"></div>
|
||
</header>
|
||
|
||
<div class="mid">
|
||
|
||
<nav>
|
||
<div id="menuWide" class="menu"></div>
|
||
<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
|
||
|
||
<div id="search" role="search"></div>
|
||
<div id="linkto"></div>
|
||
|
||
<div id="menuSlim" class="menu"></div>
|
||
<div id="menuTiny" class="menu"></div>
|
||
</nav>
|
||
|
||
<div id="extra"></div>
|
||
|
||
<article id="content" role="main">
|
||
|
||
<!-- #BeginEditable "Body" -->
|
||
|
||
|
||
<h1 class="center">Cone</h1>
|
||
|
||
<p class="center"><i>Go to <a href="#Area">Surface Area</a> or <a href="#Volume">Volume</a>.</i></p>
|
||
<div class="flexx">
|
||
<div class="col def" style="text-align:left; margin:0; width:240px;">
|
||
|
||
<h3 style="margin: 5px; padding: 5px; font-weight: bold; text-align:center; ">Cone Facts</h3>
|
||
<p><b>Notice these interesting things:</b></p>
|
||
<ul>
|
||
<li>It has a circle at one end</li>
|
||
<li>And a point at the other end</li>
|
||
<li>And a curved side</li>
|
||
<li>It is <b>not</b> a <a href="polyhedron.html">polyhedron</a> as it
|
||
has a curved surface</li>
|
||
</ul>
|
||
<p class="center"><img src="images/cone-shiny.jpg" alt="cone shiny" height="193" width="170"></p>
|
||
</div>
|
||
<div class="col" style="width: 460px;">
|
||
<div class="script" style="height: 460px;">
|
||
images/poly-gl.js?mode=cone
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/cone-apex-base.svg" alt="cone apex and base" height="196" width="210"></p>
|
||
<p> </p>
|
||
<ul>
|
||
<li>The pointy end of a cone is called the <b>apex</b></li>
|
||
<li>The flat part is the <b>base</b></li>
|
||
</ul><div style="clear:both"></div>
|
||
<div class="words">
|
||
<p>An object shaped like a cone is said to be <b>conical</b></p>
|
||
</div>
|
||
<div style="float:left; margin: 0 10px 5px 0; width:300px;">
|
||
<div class="script" style="height: 280px;">images/cone-sweep.js</div>
|
||
</div>
|
||
|
||
|
||
<h2>A Cone is a Rotated Triangle</h2>
|
||
|
||
<p>A cone can be made by rotating a triangle!</p>
|
||
<p>The triangle is a <a href="../right_angle_triangle.html">right-angled triangle</a>, and it gets rotated around one of its two short sides.</p>
|
||
<p>The side it rotates around is the <b>axis</b> of the cone.</p>
|
||
<div style="clear:both"></div>
|
||
|
||
|
||
<h2>Right vs Oblique Cone</h2>
|
||
|
||
<p>When the apex is aligned on the center of the base it is a Right Cone otherwise it is an Oblique Cone:</p>
|
||
<p class="center"><img src="images/cone-oblique.svg" alt="right vs oblique cone" height="245" width="294"></p>
|
||
<a id="Area"></a>
|
||
|
||
|
||
<h2>Surface Area of a Cone</h2>
|
||
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/cone-dimensions.svg" alt="cone dimensions h=height, r=radius, s=side length" height="226" width="233"></p>
|
||
<p>The Surface Area has two parts:</p>
|
||
<ul>
|
||
<li>The <i>Base Area</i> = <span class="times">π</span> × r<sup>2</sup></li>
|
||
<li>The <i>Side Area</i> = <span class="times">π</span> × r × s</li>
|
||
</ul>
|
||
<p>Which together makes:</p>
|
||
<p class="center large">Surface Area = <span class="times">π</span> × r × (r + s)</p>
|
||
Note: we can calculate <b>s = √(r<sup>2</sup>+h<sup>2</sup>)</b>
|
||
<div style="clear:both"></div>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example: h = 7 and r = 2</h3>
|
||
<div class="tbl">
|
||
<div class="row"><span class="left">Surface Area of Base</span><span class="right">= <span class="times">π</span> × r<sup>2</sup> </span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= <span class="times">π</span> × 2<sup>2</sup> </span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= 4<span class="times">π</span></span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">≈ <b>12.57</b></span></div>
|
||
</div>
|
||
<p> </p>
|
||
<div class="tbl">
|
||
<div class="row"><span class="left">Surface Area of Side</span><span class="right">= <span class="times">π</span> × r × √(r<sup>2</sup>+h<sup>2</sup>)</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= <span class="times">π</span> × 2 × √(2<sup>2</sup>+7<sup>2</sup>)</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= <span class="times">π</span> × 2 × √(4+49)</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= 2<span class="times">π</span>√(53)</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">≈ <b>45.74</b></span></div>
|
||
</div>
|
||
<p>Total Surface Area ≈ 12.57 + 45.74 ≈ <b>58.31</b></p>
|
||
</div>
|
||
<a id="Volume"></a>
|
||
|
||
|
||
<h2>Volume of a Cone</h2>
|
||
|
||
<p class="center large">Volume = <span class="intbl">
|
||
<em>1</em>
|
||
<strong>3</strong>
|
||
</span> <span class="times"> π</span> × r<sup>2 </sup>× h</p>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example: h = 7 and r = 2</h3>
|
||
<div class="tbl">
|
||
<div class="row"><span class="left">Volume</span><span class="right">= <span class="intbl">
|
||
<em>1</em>
|
||
<strong>3</strong>
|
||
</span> <span class="times"> π</span> × r<sup>2</sup> × h</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= <span class="intbl">
|
||
<em>1</em>
|
||
<strong>3</strong>
|
||
</span> <span class="times"> π</span> × 2<sup>2</sup> × 7</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= <span class="intbl">
|
||
<em>28</em>
|
||
<strong>3</strong>
|
||
</span> <span class="times"> π</span></span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">≈ <b>29.32</b></span></div>
|
||
</div>
|
||
</div>
|
||
<p>Play with it here. The formula also works when it "leans over" (<i>oblique</i>) but remember that the height is always at right angles to the base:</p>
|
||
<iframe src="icone.html" scrolling="no" style="background-color:white; width:362px; height:302px; overflow:hidden; margin:auto; display:block; border: none; text-align:center;"></iframe>
|
||
|
||
|
||
<h2>Volume of a Cone vs Cylinder</h2>
|
||
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/cone-vs-cylinder.svg" alt="cone vs cylinder" height="126" width="232"></p>
|
||
<p>The volume formulas for cones and <a href="cylinder.html">cylinders</a> are very similar:</p>
|
||
<div class="simple">
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr valign="middle">
|
||
<td style="text-align:right;">The volume of a cylinder is: </td>
|
||
<td style="text-align:right;"><span class="larger"><span class="times"> π</span> × r<sup>2 </sup>× h</span></td>
|
||
</tr>
|
||
<tr valign="middle">
|
||
<td style="text-align:right;">The volume of a cone is: </td>
|
||
<td style="text-align:right;"><span class="larger"> <span class="intbl">
|
||
<em>1</em>
|
||
<strong>3</strong>
|
||
</span> <span class="times"> π</span> × r<sup>2 </sup>× h</span></td>
|
||
</tr>
|
||
</tbody></table>
|
||
</div>
|
||
<p>So a cone's volume is exactly one third (
|
||
<span class="intbl">
|
||
<em>1</em>
|
||
<strong>3</strong>
|
||
</span>
|
||
) of a cylinder's volume.</p>
|
||
<p>You should order your ice creams in cylinders, not cones, you get 3 times as much!</p>
|
||
|
||
|
||
<h2>Like a Pyramid</h2>
|
||
|
||
<p>A cone is also like a pyramid with an infinite number of sides, see <a href="pyramid-vs-cone.html">Pyramid vs Cone</a>.</p>
|
||
|
||
|
||
<h2>Different Shaped Cones</h2>
|
||
|
||
<p class="center"><img src="images/cone-wood1.jpg" alt="wooden cone narrow" height="220" width="127"><img src="images/cone-wood3.jpg" alt="wooden cone medium" height="220" width="173"><img src="images/cone-wood4.jpg" alt="wooden cone wide" height="220" width="199"></p>
|
||
|
||
|
||
<h2>Construction Cone</h2>
|
||
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/cone-construction.svg" alt="Construction Cone" height="168" width="129"></p>
|
||
<p>This is <i><b>almost</b></i> a cone, but the top is chopped off (called a "truncated cone").</p>
|
||
<p>Also it has a wider base added so it doesn't fall over!</p>
|
||
<div style="clear:both"></div>
|
||
<div class="questions">873,874,875,876, 1833, 1834, 3399, 3400, 3401, 3402</div>
|
||
|
||
<div class="related">
|
||
<a href="pyramid-vs-cone.html">Pyramid vs Cone</a>
|
||
<a href="cylinder.html">Cylinder</a>
|
||
<a href="sphere.html">Sphere</a>
|
||
<a href="cone-sphere-cylinder.html">Cone vs Sphere vs Cylinder</a>
|
||
<a href="torus.html">Torus</a>
|
||
<a href="prisms.html">Prisms</a>
|
||
<a href="polyhedron.html">Polyhedron</a>
|
||
<a href="../platonic_solids.html">Platonic Solids</a>
|
||
</div>
|
||
<!-- #EndEditable -->
|
||
|
||
</article>
|
||
|
||
<div id="adend" class="centerfull noprint"></div>
|
||
<footer id="footer" class="centerfull noprint"></footer>
|
||
<div id="copyrt">Copyright © 2022 Rod Pierce</div>
|
||
|
||
</div>
|
||
</body><!-- #EndTemplate -->
|
||
<!-- Mirrored from www.mathsisfun.com/geometry/cone.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:39 GMT -->
|
||
</html> |