circular cross-section of log

The figure shows the circular cross-section of a uniform log of radius \(\quantity{40}{cm}\) floating in water. The points \(A\) and \(B\) are on the surface and the highest point \(X\) is \(\quantity{8}{cm}\) above the surface.

Show that \(\widehat{AOB}\) is approximately \(1.29\) radians.


  1. the length of the arc \(AXB\),
  2. the area of the cross-section below the surface,
  3. the percentage of the volume of the log below the surface.