The curve \(C\) is defined parametrically by \(x=18t-t^2\) and \(y=8t^{3/2}\), where \(0\lt t\lt4\).

(i) Show that, at all points of \(C\), \(\frac{d^2y}{dx^2}=\frac{3(9+t)}{2t^{1/2}(9-t)^3}\).

(ii) Show that the mean value of \(\frac{d^2y}{dx^2}\) with respect to \(x\) over the interval \(0\le x\le56\) is \(\frac{3}{70}\).

(iii) Find the area of the surface generated when \(C\) is rotated through \(2\pi\) radians about the \(x\)-axis, showing full working.