Just \(K\)?

Calculus Level pending

Let \(R\) be the region enclosed by the coordinate axes and the graph of \(y = K(x-2)^2 \).

When \(R\) is revolved \(360^\circ\) about the \(y\)-axis, the solid formed has a volume of \(8\pi\text{ unit}^3\). Find the positive value of \(K\).

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