The following is almost certainly going to seem a bit confusing until you’ve seen a fair few examples. Don’t stress now, just try and picture what’s going on and we will build up our understanding as we go along.
Having understood how to calculate the areas between two curves, or simply the area under a curve as a limit of the Riemann sum we can start to think about how to approximate not areas but volumes. If we can calculate an area by adding together small rectangles, perhaps we can calculate volumes by adding together small boxes, or other shapes. In fact we will use not boxes but cylinders, though perhaps not cylinders as we normally think of them.
You probably think of a cylinder as a tube with a circular cross-section, but in fact that is a particular type of cylinder called a circular cylinder. The general idea of a cylinder is a three dimensional object with a constant cross section.…