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185 lines
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<title>Cuboids, Rectangular Prisms and Cubes</title>
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<h1 align="center">Cuboids, Rectangular Prisms and Cubes</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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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/cuboid-lwh.svg" alt="cuboid" /></p>
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<p class="larger">A <b>cuboid</b> is a box-shaped object. </p>
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<p>It has six flat faces and all angles are <a href="../rightangle.html">right angles</a>.</p>
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<p>And all of its faces are rectangles.</p>
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<p>It is also a <a href="prisms.html">prism</a> because it has the same cross-section along a length. In fact it is a <b>rectangular prism</b>.</p>
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<p> </p>
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<h2>Examples of Cuboids</h2>
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<p>Cuboids are very common in our world, from boxes to buildings we see them everywhere. We can even fit them inside other cuboids!</p>
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<div class="boxa"> <img src="images/cuboid-building.jpg" width="96" height="150" alt="cuboid building" /><br>
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A building</div> <div class="boxa"> <img src="images/cuboid-apple-box.jpg" width="114" height="150" alt="cuboid apple box" /><br>
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A box with a <br>
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slot as a handle </div>
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<div class="boxa"> <img src="images/cuboid-cornell-box.jpg" width="150" height="150" alt="cuboid boxes" /><br>
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Cuboids in a <br>
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cuboid room </div>
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<div class="boxa"> <img src="images/cuboid-train-boxes.jpg" width="177" height="150" alt="cuboid model train boxes" /><br>
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Boxes for model trains </div>
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<div class="boxa"><img src="images/cuboid-mpossible.svg" alt="cuboid impossible" /><br>
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Now that's just silly! </div><p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"><a href="cuboids-rectangular-prisms.html"><img src="images/blue-cuboid.jpg" width="200" height="169" border="0" alt="cuboid" /></a></p>
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<h2>Square Prism
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</h2>
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<p>When at least two of the lengths are equal it can also be called a <b>square prism</b>.</p>
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<p>(Note: we can still call it a rectangular prism if we want!)</p>
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<div style="clear:both"></div>
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<p style="float:right; margin: 0 0 5px 10px;"><a href="hexahedron.html"><img src="images/blue-cube.jpg" width="190" height="190" border="0" alt="cube" /></a></p>
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<h2>Cube</h2>
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<p>When all three lengths are equal it is called a <b><a href="hexahedron.html">cube</a></b><a href="hexahedron.html"> (or hexahedron)</a> <br />
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and each face is a square.</p>
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<p>A cube is still a prism.</p>
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<p>And a cube is one of the <a href="../platonic_solids.html">Platonic Solids</a>.</p>
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<p > </p>
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So:
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<ul>
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<div class="bigul">
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<li>A cube is just a special case of a square prism, and<br />
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</li>
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<li>A square prism is just a special case of a rectangular prism, and<br />
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</li>
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<li>They are all cuboids! </li>
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</div>
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<br />
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</ul>
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<div class="words">
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<p>Note: The name "cuboid" comes from "cube"<b> </b>and <i><b>-oid</b></i> (which means "similar to, or resembling") and so says "it is <i>like</i> a cube". </p>
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<p>Another use of <b><i>-oid</i></b> is when we talk about the Earth being a spheroid (not exactly a sphere, but close).</p>
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</div>
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<a id="Area"></a>
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<h2>Surface Area</h2>
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<p>The surface area is found using the formula:</p>
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<p class="center larger">Area = 2 × Width × Length + 2 × Length × Height + 2 × Width × Height</p><p style="float:left; margin: 0 10px 5px 0;"><img src="images/cuboid-area.gif" width="160" height="211" alt="cuboid area 2wl 2lh and 2hw" /></p>
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<p> </p>
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<p class="center">Which can be shortened to: </p>
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<p align="center"><span class="largest">A = 2wl + 2lh + 2hw</span></p>
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<div style="clear:both"></div>
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<div class="example">
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<h3>Example: Find the surface area of this cuboid</h3>
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<p class="center"><img src="images/cuboid-example.svg" alt="cuboid 10x4x5" />
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</p>
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<table border="0" align="center">
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<tr>
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<td><span class="larger">A</span></td>
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<td width="30" align="center"><span class="larger"> = </span></td>
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<td><span class="larger"> 2wl + 2lh + 2hw</span></td>
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</tr>
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<tr>
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<td> </td>
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<td width="30" align="center"><span class="larger">=</span></td>
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<td><span class="larger">2×4×10 + 2×10×5 + 2×5×4</span></td>
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</tr>
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<tr>
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<td> </td>
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<td width="30" align="center"><span class="larger">=</span></td>
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<td><span class="larger">80 + 100 + 40 </span></td>
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</tr>
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<tr>
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<td> </td>
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<td width="30" align="center"><span class="larger">=</span></td>
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<td><span class="larger">220 </span></td>
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</tr>
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</table>
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</div>
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<a id="Volume"></a>
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<h2>Volume</h2>
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<p>The <a href="../cuboid.html">volume of a cuboid</a> is found using the formula:</p>
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<p align="center"> <span class="larger">Volume = Length × Width × </span> <span class="larger">Height</span></p>
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<p>Which<span class="center"> can be </span> shortened to: </p>
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<p align="center" class="largest">V = l × w × h</p>
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<p align="left">Or more simply:</p>
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<p align="center" class="largest">V = lwh</p>
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<div class="example">
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<h3>Example: Find the volume of this cuboid</h3>
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<table border="0" align="center">
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<tr>
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<td><img src="images/cuboid-example.svg" alt="cuboid 10x5x4" /></td>
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<td> </td>
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<td nowrap><div class="larger">V = lwh<br />
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= 10×4×5<br />
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= 200</div></td>
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</tr>
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</table>
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</div>
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<p style="float:left; margin: 0 10px 5px 0;"> </p>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(859,860,1816, 1817, 1818, 1819, 1820, 1821, 1822, 1823);</script> </div>
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<div class="related"> <a href="hexahedron.html">Cube (Hexahedron)</a> <a href="prisms.html">Prisms</a> <a href="index.html">Geometry Index</a> </div>
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