The finite region enclosed by the line \(y=k x\), where \(k\) is a positive constant, the \(x\)-axis is and the line \(x=h\) is rotated through 1 complete revolution about the \(x\)-axis. Prove by integ. the centroid of the resulting cone is at a distance \(\frac{3}{4} h\) from the origin \(O\).
[The volume of a cone of height \(h\) and base radius \(r\) is \(\frac{1}{3} \pi r^{2} h\).]