A vacuum flask (for keeping drinks hot) is modelled as a closed cylinder in which the internal radius is \(r\) cm and the internal height is \(h\) cm. The volume of the flask is 1000 cm\(^3\). A flask is most efficient when the total internal surface area, \(A\) cm\(^2\), is a minimum.

(i) Show that \(A = 2\pi r^2 + \frac{2000}{r}\).

(ii) Given that \(r\) can vary, find the value of \(r\), correct to 1 decimal place, for which \(A\) has a stationary value and verify that the flask is most efficient when \(r\) takes this value.