We have found (or approximated) the volume of a rotated flag with various shapes. What if the axis of rotation (the "pole") is not attached directly to the flag?
In the graph above, there is a gap between the flag and the x-axis. Decide what will occur when this flag is rotated about the x-axis. Draw a sketch of the result and find the volume of the resulting solid. To help you visualize this, use the 2-121 eTool (Desmos). Homework Help ✎
A large cylinder, with a hollow cylindrical hole in the center.
Compute two volumes and subtract: a large solid cylinder − the cylindrical hole.
Both cylinders have a height of 3.
The large cylinder has a radius of 2. The small cylinder has a radius of 1.
Use the eTool below to visualize the flag.
Click the link at right for the full version of the eTool: Calc 2-121 HW eTool