6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{00776cc0-0214-4029-8ef1-c1cba89f4b87-4_455_540_201_660}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
Figure 3 shows part of the curve \(y = x ^ { 2 } + 1\). The shaded region enclosed by the curve, the coordinate axes and the line \(x = 1\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
- Find the coordinates of the centre of mass of the solid obtained.
The solid is suspended from a point on its larger circular rim and hangs in equilibrium.
- Find, correct to the nearest degree, the acute angle which the plane surfaces of the solid make with the vertical.
(3 marks)