The base of a right cylinder is the circle in the xy-plane with centre O and radius 3 units. A wedge is obtained by cutting this cylinder with the plane through the y-axis inclined at 60^{0} to the xy-plane, as shown in the diagram.
(a) A rectangular slice ABCD is taken perpendicular to the base of the wedge at a distance x from the y-axis. If the slice is xδ thick, show that the volume of the slice is given by
(b) Explain why the volume of the wedge may be represented by dx Evaluate this integral, using calculus methods, to find the exact volume of the wedge.