actually should my answer be 1114?
Hi wolfhound.
It always helps to understand how the situation looks on a diagram.
The volume of revolution is the sum of the areas of a series of "wafer-thin" discs (an "infinite" sum of them, evaluated as their widths "deta-x" goes to zero).
The radius of the discs in this case is f(x) because the curve is being rotated around the x-axis.
the area of a disc is
All of these disc areas are integrated from x=0 to x=3.
This gives the volume of revolution.
You need to get used to how to do this notationally,
as your written work needs to be redone.
Therefore, the volume of revolution is
from x=0 to 3
I've shown the disc from an angle (hence it looks like an ellipse!)