Volume of a Solid of Revolution

Problem

S is a surface generated by revolving a line segment AB about z-axis where A is (2,-1,0) and B is (1,2,3). Find the volume of the solid surrounded by S, z=0, and z=3.

Applet

Rotation: "Animate" button shows the revolution of the line segment about the z-axis.
A Cross-Section: It shows the solid of revolution and a cross-section.
To move the cross-section, click "+" and "-" button.

Solution

Real Model

I bought it at AMI conference.