6 The diagram shows a cylindrical container of radius \(r \mathrm {~cm}\) and height \(h \mathrm {~cm}\). The container has an open top and a circular base.
\includegraphics[max width=\textwidth, alt={}, center]{c7f38f7e-75aa-4b41-96fd-f38f968c225c-12_389_426_404_751} The external surface area of the container's curved surface and base is \(48 \pi \mathrm {~cm} ^ { 2 }\).
When the radius of the base is \(r \mathrm {~cm}\), the volume of the container is \(V \mathrm {~cm} ^ { 3 }\).

1. 1. Find an expression for \(h\) in terms of \(r\).
   2. Show that \(V = 24 \pi r - \frac { \pi } { 2 } r ^ { 3 }\).
2. 1. Find \(\frac { \mathrm { d } V } { \mathrm {~d} r }\).
   2. Find the positive value of \(r\) for which \(V\) is stationary, and determine whether this stationary value is a maximum value or a minimum value.
      [0pt] [4 marks]