The diagram shows part of the graph of

\(y=16x+\frac{27}{x^2},\)

which has a minimum at \(A\).

(i) Find the coordinates of \(A\).

The points \(P\) and \(Q\) lie on the curve \(y=16x+\dfrac{27}{x^2}\) and have \(x\)-coordinates \(1\) and \(3\) respectively.

(ii) Find the area enclosed by the curve and the line \(PQ\). You must show all your working.