Volume of revolution yielded by region between two curves

The diagram shows the region \(R\) in the first quadrant enclosed by the curves \(y = \frac{1}{4}(4 - x^2)\), \(y = \frac{1}{2}(4 - x^2)\) and the \(y\)-axis.

Calculate the volume of revolution formed when \(R\) is rotated through \(360{}^\circ\) about the \(y\)-axis.