A curve \(C\) has parametric equations
\(x=\frac{2}{5} t^{\frac{5}{2}}-2 t^{\frac{1}{2}}, \quad y=\frac{4}{3} t^{\frac{3}{2}}, \quad \text { for } 1 \leqslant t \leqslant 4\)
(i) Find the exact value of the arc length of \(C\).

(ii) Find also the exact value of the surface area generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.