Volume of the solid formed by rotating the region under a quarter-ellipse curve about the y-axis

The diagram shows part of the curve \(y=\sqrt{9\left(1-\frac{x^2}{4}\right)}\), drawn for \(0\leq x\leq2\). The curve meets the \(y\)-axis at the point \((0,a)\).

1. Write down the value of \(a\).[1]
2. Let \(R\) be the region enclosed by the curve and the two coordinate axes. A solid is generated when \(R\) is turned through \(360^\circ\) about the \(y\)-axis.
   Find the volume of the solid generated.[5]