2021 TMJC P1 Q3

Two curves \({{C}_{1}}\) and \({{C}_{2}}\) have equations \(y=-\sqrt{\left( 1-\frac{{{\left( x-2 \right)}^{2}}}{4} \right)}\) and \(y=-\frac{1}{4}{{x}^{2}}\) respectively.

1. Sketch \({{C}_{1}}\) and \({{C}_{2}}\) on the same diagram, stating the coordinates of any axial intercepts and points of intersections between \({{C}_{1}}\) and \({{C}_{2}}\) .[3]
2. The region \(R\) is bounded by \({{C}_{1}}\) and \({{C}_{2}}\). Find the volume of the solid of revolution formed when \(R\) is rotated through \(2\pi \) radians about the \(x\)-axis.[3]