A uniform right solid circular cone \(C\) has radius \(r\) and height \(4 r\).
- Show, using algebraic integration, that the distance of the centre of mass of \(C\) from its vertex is \(3 r\).
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[You may assume that the volume of \(C\) is \(\frac { 4 } { 3 } \pi r ^ { 3 }\) ]
A uniform solid \(S\), shown below in Figure 3, is formed by removing from \(C\) a uniform solid right circular cylinder of height \(r\) and radius \(\frac { 1 } { 2 } r\), where the centre of one end of the cylinder coincides with the centre of the plane face of \(C\) and the axis of the cylinder coincides with the axis of \(C\).
\begin{figure}[h]
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\caption{Figure 3}
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