6 A uniform solid is formed by rotating the region enclosed by the positive \(x\)-axis, the line \(x = 2\) and the curve \(y = \frac { 1 } { 2 } x ^ { 2 }\) through \(360 ^ { \circ }\) around the \(x\)-axis.
6
- Find the centre of mass of this solid.
6 - The solid is placed with its plane face on a rough inclined plane and does not slide. The angle between the inclined plane and the horizontal is gradually increased.
When the angle between the inclined plane and the horizontal is \(\alpha\), the solid is on the point of toppling.
Find \(\alpha\), giving your answer to the nearest \(0.1 ^ { \circ }\)