The region \(A\) is bounded by the \(x\)-axis, the \(y\)-axis, the curve \(y = \sqrt { x ^ { 2 } + 16 }\) and the line \(x = 3\). The region \(B\) is bounded by the \(y\)-axis, the curve \(y = \sqrt { x ^ { 2 } + 16 }\) and the line \(y = 5\). These regions are shown in Fig. 4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{70a2c3ce-7bdb-4ddd-92fc-f7dcbdfdcfaf-5_604_460_605_792}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
- Find the \(x\)-coordinate of the centre of mass of the uniform solid of revolution formed when the region \(A\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
- Using your answer to part (i), or otherwise, find the \(x\)-coordinate of the centre of mass of the uniform solid of revolution formed when the region \(B\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
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