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.
(i)
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]
(ii)
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]
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