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A closed cylindrical metal box has a radius of \(r\) centimetres and a height of \(h\) centimetres, with a volume of \(20\pi\, cm^3\).

The figure is not to scale.

1. Express \(h\) in terms of \(r\).

The metal for the base and lid of the box costs 10 cents per \(cm^2\).

The metal for the curved side costs \(8\) cents per \(cm^2\).

The total cost of the metal, in cents, is \(C\).

2. Show that \(C\,=\,20\pi{}r^2 + \frac{320\pi}{r}\)
3. Given that a minimum value of \(C\) exists, find this minimum value in terms of \(\pi\).