2025 VJC P1 Q9

In the diagram below, the region \(R\) is bounded by the curve \(C\) with equation \(x = 6 - (y-2)^2\), the lines \(y = 8\), \(y = 2 - x\) and the \(y\)-axis. The region \(S\) is bounded by \(C\) and the line \(y = 2 - x\).

1. Find the exact area of region \(R\).[5]
2. Find the volume of the solid of revolution formed when region \(S\) is rotated through \(360{}^\circ\) about the \(x\)-axis, leaving your answer to \(2\) decimal places.[3]