6 A uniform solid consists of a hemisphere with centre \(O\) and radius 0.6 m joined to a cylinder of radius 0.6 m and height 0.6 m . The plane face of the hemisphere coincides with one of the plane faces of the cylinder.
- Calculate the distance of the centre of mass of the solid from \(O\).
[0pt]
[The volume of a hemisphere of radius \(r\) is \(\frac { 2 } { 3 } \pi r ^ { 3 }\).]
\includegraphics[max width=\textwidth, alt={}, center]{a093cbad-3ba0-45ce-a617-d4ecc8cb1ec9-4_547_631_593_797}
A cylindrical hole, of length 0.48 m , starting at the plane face of the solid, is made along the axis of symmetry (see diagram). The resulting solid has its centre of mass at \(O\). Show that the area of the cross-section of the hole is \(\frac { 3 } { 16 } \pi \mathrm {~m} ^ { 2 }\).- It is possible to increase the length of the cylindrical hole so that the solid still has its centre of mass at \(O\). State the increase in the length of the hole.