N1995 P1 Q17

A curve \(C\) has equation \(y=\frac{1}{\sqrt{4-{{x}^{2}}}}\) for \(-1\le x\le 1\). The region \(R\) is enclosed by \(C\), the \(x\)- axis and the lines \(x=-1\) and \(x=1\).

1. Find the exact value of the area of \(R\).[3]
2. Find the exact value of the volume generated when \(R\) is rotated through two right angles about the \(x\)- axis.[3]
3. Show that the volume generated when \(R\) is rotated through two right angles about the \(y\)- axis is \(\pi \,(4-2\sqrt{3})\).[4]