Show that the distance \(d\) of the centre of mass of the toy from its lowest point \(O\) is given by
$$d = \frac { h ^ { 2 } + 2 h r + 5 r ^ { 2 } } { 2 ( h + 4 r ) } .$$
When the toy is placed with any point of the curved surface of the hemisphere resting on the plane it will remain in equilibrium.