Ratio of surface areas

Geometry Level 2

The total surface area and the curved surface area of a cylinder that is open at the top are in the ratio \(3:1 \). What is the ratio of the radius of the cylinder to that of the height?

If your answer is the form of \(a: b\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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