### Home > CALC > Chapter 2 > Lesson 2.3.2 > Problem 2-121

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 at right, there is a gap between the flag and the *x*-axis. Decide what will occur when this flag is rotated about the -axis. Draw a sketch of the result and find the volume of the resulting solid. To help you visualize this, use the .

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

The large cylinder has a radius of

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*