The diagram shows a solid cone which has a slant height of 15 cm and a vertical height of h cm.

(i) Show that the volume, V cm³, of the cone is given by \(V = \frac{1}{3}\pi(225h - h^3)\).

[The volume of a cone of radius r and vertical height h is \(\frac{1}{3}\pi r^2 h\).]

(ii) Given that h can vary, find the value of h for which V has a stationary value. Determine, showing all necessary working, the nature of this stationary value.