Hi Colleen,
I plotted a sketch of y = x^{3}, y = 8 and x = 1 and shaded the region R.
The region shaded orange is the region you need to revolve around the yaxis. Either the disk or shell method will work but I think in this situation the cylindrical shell method results in an easier integral.
To use the cylindrical shell method take a vertical slice through the region R of thickness x and revolve this slice around the yaxis.
Is this enough help? Let us know.
Penny
