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      <text>14.3.1.1 Volumes generated by rotating curves about the x-axis</text>
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      <text><![CDATA[<h3>Volumes generated by rotating curves about the x-axis</h3>

<p>The figure below shows a graph of the function \(y=2x\) for \(x\) between 0 and 3.</p><p style="text-align: center;"><img src="@@PLUGINFILE@@/14-3-fig-8-linegraph.svg" alt="A graph of the function y = 2x, for x between 0 and 3." width="145" height="128" class="img-responsive atto_image_button_text-bottom"><br></p>
<p>Imagine rotating the line \(y=2x\) by one complete revolution (\(360^{\circ}\) or \(2\pi\) radians) around the \(x\)-axis. The surface so formed is the surface of a cone as shown in the figure below. Such a three-dimensional shape is known as a <strong>solid of revolution</strong>.
    We now discuss how to obtain the volumes of such solids of revolution.</p><p style="text-align: center;"><img src="@@PLUGINFILE@@/14-3-fig-9-conerevolution.svg" alt="When line y = 2x is rotated around the axis a solid is generated. It's a cone, vertex at origin, axis = x-axis, base at x=3." width="199" height="261" class="img-responsive atto_image_button_text-bottom"><br></p>]]></text>
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