Spinning a Circle, along a Circle!
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.