Spinning a Circle, along a Circle!

Geometry Level 4

Consider a circle of variable radius which is displaced in such a way that one of the points of its circumference remains fixed on the \(x\)-axis and its centre moves along the circle \( x^2+ y^2 = 4 \). Also, the plane containing this circle is perpendicular to the \(x\)-axis.

Find the closed form of the volume of this solid.

Give your answer to 4 decimal places.

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