OME 1968 Problem 4

At the two ends $A, B$ of a diameter (of length $2r$ ) of a pavement horizontal circular rise two vertical columns, of equal height h, whose ends support a beam $A' B'$ of length equal to the before mentioned diameter. It forms a covered by placing numerous taut cables (which are admitted to be rectilinear), joining points of the beam $A'B'$ with points of the circumference edge of the pavement, so that the cables are perpendicular to the beam $A'B'$ . You want to find out the volume enclosed between the roof and the pavement.