The dimensions of a cuboid are x cm, 2x cm and 4x cm, as shown in the diagram.

(i) Show that the surface area S cm² and the volume V cm³ are connected by the relation

\(S = 7V^{\frac{2}{3}}\).

(ii) When the volume of the cuboid is 1000 cm³ the surface area is increasing at 2 cm² s⁻¹. Find the rate of increase of the volume at this instant.