A cone of radius \(r\) cm and vertical height \(h\) cm has volume \(V=\dfrac13\pi r^2h\) and \(h=\dfrac32r\). Find the rate of increase of the height of this cone when the radius is 6 cm and the volume is increasing at a rate of \(4\pi\text{ cm}^3/\text{s}\).[6]
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