2021 DHS P1 Q4

The diagram shows the shaded region \(R\) bounded by curve \(C\) with equation \(x=\frac{1}{\sqrt{1-{{y}^{2}}}}\) and the line \(x=2\).

1. Find the exact volume of the solid generated when \(R\) is rotated through \(2\pi \) radians about the \(y\)-axis.[5]
2. Write down the equation of the curve obtained when \(C\) is translated by \(2\) units in the negative \(x\)-direction. Hence, or otherwise, find the volume of the solid generated when \(R\) is rotated through \(2\pi \) radians about the line \(x=2\).[3]