(a) To find the coordinates of \(A\), substitute \(x = 0\) into the circle equation \((x-2)^2 + y^2 = 8\):

\((-2)^2 + y^2 = 8\)

\(4 + y^2 = 8\)

\(y^2 = 4\)

\(y = 2\) (since \(A\) is on the positive \(y\)-axis)

Thus, \(A = (0, 2)\).

For \(B\), since \(AB\) is parallel to the \(x\)-axis, \(y = 2\). Substitute \(y = 2\) into the circle equation:

\((x-2)^2 + 4 = 8\)

\((x-2)^2 = 4\)

\(x-2 = \pm 2\)

\(x = 4\) (since \(B\) is on the right side of the circle)

Thus, \(B = (4, 2)\).

(b) The volume of revolution is found by integrating the area of the segment rotated about the \(x\)-axis:

Volume = \(\pi \int_0^4 (8 - (x-2)^2) \, dx\)

\(= \pi \left[ 8x - \frac{(x-2)^3}{3} \right]_0^4\)

\(= \pi \left[ 32 - \frac{16}{3} \right]\)

Volume of cylinder = \(\pi \times 2^2 \times 4 = 16\pi\)

Total volume = \(26\frac{2}{3}\pi - 16\pi = 10\frac{2}{3}\pi\)