The diagram shows part of the curve \(y = x + \frac{4}{x}\) which has a minimum point at \(M\). The line \(y = 5\) intersects the curve at the points \(A\) and \(B\).

(i) Find the coordinates of \(A, B\) and \(M\).

(ii) Find the volume obtained when the shaded region is rotated through 360° about the x-axis.