1.
State from which point of the body you're taking moments from - this makes life a little easier for the examiner
2.
Start using mass ratios! The algebra becomes a lot simpler.
\displaystyle [br]\begin{equation*}\bar{x} = 3r - \frac{216r^2 - 12hr + h^2}{4(36r - h)} = \cdots = \frac{216r^2 - h^2}{4(36r - h)}\end{equation*}
\displaystyle [br]\begin{equation*}\bar{x} = 3r - \frac{216r^2 - 12hr + h^2}{4(36r - h)} = \cdots = \frac{216r^2 - h}{4(36r - h)}\end{equation*}
1.
State from which point of the body you're taking moments from - this makes life a little easier for the examiner
2.
Start using mass ratios! The algebra becomes a lot simpler.
\displaystyle [br]\begin{equation*}\bar{x} = 3r - \frac{216r^2 - 12hr + h^2}{4(36r - h)} = \cdots = \frac{216r^2 - h}{4(36r - h)}\end{equation*}