5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ae189c40-0071-4a6b-91eb-8ffebe082a04-16_492_442_237_744}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

The region $R$, shown shaded in Figure 3, is bounded by the circle with centre $O$ and radius $r$, the line with equation $x = \frac { 3 } { 5 } r$ and the $x$-axis. The region is rotated through one complete revolution about the $x$-axis to form a uniform solid $S$.
\begin{enumerate}[label=(\alph*)]
\item Use algebraic integration to show that the $x$ coordinate of the centre of mass of $S$ is $\frac { 48 } { 65 } r$.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ae189c40-0071-4a6b-91eb-8ffebe082a04-16_394_643_1311_653}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

A bowl is made from a uniform solid hemisphere of radius 6 cm by removing a hemisphere of radius 5 cm . Both hemispheres have the same centre $A$ and the same axis of symmetry. The bowl is fixed with its open plane face uppermost and horizontal. Liquid is poured into the bowl. The depth of the liquid is 2 cm , as shown in Figure 4. The mass of the empty bowl is $5 M \mathrm {~kg}$ and the mass of the liquid is $2 M \mathrm {~kg}$.
\item Find, to 3 significant figures, the distance from $A$ to the centre of mass of the bowl with its liquid.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2019 Q5 [16]}}