If the region to be revolved is not bordered by the axis, the section of the solid is not a disk, but an annulus.
Denote by the function whose graph is the outer boundary of the region , and by the function whose graph is the inner boundary of ; suppose that both functions are continuous on , where .
We revolve about the axis the region bounded by the parabolas whose respective equations are and , by the axis and the line whose equation is , i.e. the region in Figure 7.
The volume of the solid is given by:
Noah Dana-Picard 2007-12-28