Annulus Volume of Revolution

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A segment of a circle is created using a chord parallel to the x-axis. The resulting segment of the circle is then revolved 360° about the x-axis. The problem is to calculate the volume of the resulting annulus.

To find a general solution to the problem involves using an elemental disc ring and integrating with respect to dx. The end result is somewhat surprising in that it does not include the radius of the circle.

Supporting resources include a video and autograph file. These help demonstrate how the width of each segment is the same but the curvature of the upper edge gets smaller as the radius of the circle increases. The reduction in cross-sectional area is compensated by the further distance that is swept through.

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