When a function is rotated around a vertical line, the washers or disks are stacked in a tower-like structure. They are stacked horizontally. When a function is rotated around a horizontal line, the washers or disks are stacked next to each other. They are lined up vertically. The variable that goes with rotation around a vertical line is y and the variable that goes with rotation around a horizontal line is x.
Washers vs. Disks
The main difference between creating disks or washers when rotating a function is that washers have space in the middle. Disks have no space in the middle of the shape.
Examples
Find the volume of the region bounded by y = x2, y = 0, and x = 2 rotated about x = 3.
Find the volume of the region bounded by y = 2x - 2, y = 0, and x = 3 rotated about the x-axis.
