JPJC Tutorial Question 11

The diagram shows the shaded region \(R\) bounded by the curve \({{\left( x-3 \right)}^{2}}+{{\left( y-1 \right)}^{2}}=8\) and the line \(y=x-2\).

1. State the exact area of the region \(R\).[1]
2. Find the volume generated when region \(R\) is rotated through \(2\pi \) radians about the \(y\)-axis.[4]