(i) The curve \(y = (x - 2)^2\) is a parabola opening upwards with vertex at \((2, 0)\). It touches the positive \(x\)-axis at \(x = 2\).

(ii) To find the volume of the solid of revolution, use the formula for the volume of a solid of revolution about the \(x\)-axis: \(V = \pi \int (y)^2 \, dx\).

Here, \(y = (x - 2)^2\), so \(y^2 = (x - 2)^4\).

Calculate the integral: \(V = \pi \int_0^2 (x - 2)^4 \, dx\).

Expand \((x - 2)^4\) and integrate: \(\pi \left[ \frac{(x - 2)^5}{5} \right]_0^2\).

Evaluate the integral: \(\pi \left[ \frac{(2 - 2)^5}{5} - \frac{(-2)^5}{5} \right] = \pi \left[ 0 - \frac{-32}{5} \right] = \frac{32\pi}{5}\).

Thus, the volume is \(\frac{32\pi}{5}\) or \(6.4\pi\).