The diagram shows part of the curve $y = 4\surd x - x$. The curve has a maximum point at $M$ and meets the x-axis at $O$ and $A$.
a) Find the coordinates of $A$ and $M$.
b) Find the volume obtained when the shaded region is rotated through ${360^ \circ }$ about the x-axis, giving your answer in terms of $\pi $.

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