What's the least surface area of this rocket-shaped solid?

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A rocket-shaped solid consists of a right circular cylinder of length \(l\) and radius \(r\) attached at one end to the base of a right circular cone of base radius \(r\) and height \(\frac{3}{4}r\). If the total volume of the solid is to be \(\quantity{14\pi}{cm^3}\), find its least possible surface area.