Applications of Integration - Volume of Revolution

The curve \(C\) is given by \(y = 3\sqrt{x}\). The region \(S\) is enclosed by \(C\), the \(x\)-axis, and the line \(x = 9\). The region \(K\) is enclosed by \(C\), the \(y\)-axis, and the line \(y = 6\). Find the volume of

1. \(S\) exactly when \(S\) is rotated through \(2\pi\) radians about the \(x\)-axis;

2. \(K\) when \(K\) is rotated through \(4\) right angles about the \(y\)-axis, correct to \(4\) decimal places.