No, your rectangle, when revolved around the x-axis, will create a cylinder laying on its side. The base of the cylinder will be created by the line segment from (0,0) to (0,2). The height of the cylinder (in the x-direction) will be 3. You know the volume of this cylinder has to be .
You should have a formula in your textbook that goes something like along with some explanation and hopefully some nice pictures. Even though you can figure out the volume another way, you should know how to use integration to get the volume on this simple problem before moving to more complicated problems.