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    The Geometry of a Cycloid

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    The circle has a radius of 8. As the circle rolls along the line, the point P (a pencil point) draws a curve.

    a) Draw the curve for three complete revolutions of the circle.
    b) Find the area between the curve (one loop) and the line.
    c) Find the length of the curve - all three loops.

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    Solution Preview

    The arc length of one hump of a cycloid is marked by:

    L = 8r (where r is the radius of the circle)

    The area under the curve is marked by:

    A = ...

    Solution Summary

    The solution shows how to calculate the area of a cycloid and the length of three complete revolutions.