Fitting a cylinder inside a cone

So I think this is a related rates problem though i am not sure. I am in calculus AB.

A right circular cone has base radius 5 and altitude 12. A cylinder is to be inscribed in the cone so that the axis the cylinder coincides with the axis of the cone. given hat the radius of the cylinder must be between 2 and 4 inclusive, find the the value of that radius for which the laterals surface area of the cylinder is minimum. Justify you answer. (Note: The lateral surface of a cylinder does not include the bases)

any help to answer answer this problem? Thanks.