- The finite region enclosed by the curve with equation \(y = 3 - \sqrt { x }\) and the lines \(x = 0\) and \(y = 0\) is rotated through \(2 \pi\) radians about the \(x\)-axis, to form a uniform solid \(S\).
Use algebraic integration to
- show that the volume of \(S\) is \(\frac { 27 } { 2 } \pi\)
- find the \(x\) coordinate of the centre of mass of \(S\).