The solid `ABCD` is cut from a quarter cylinder of radius `r` as shown. Its base is an isosceles triangle `ABC` with `AB = AC`. The length of `BC` is `a` and the midpoint of `BC` is `X`.
The cross-sections perpendicular to `AX` are rectangles. A typical cross-section is shown shaded in the diagram.
Find the volume of the solid `ABCD`. (4 marks)