Let us suppose that you want to compute the volume of a solid of revolution, which is a solid formed by sweeping a two-dimensional (2D) region around an axis. This calculator will help you with this.
You may have already studied one method or another for finding the volume using the disk/washer method. Here, a solid is sliced into thin disks or washers (disks with a hole in the middle or centre).
However, the volume of some solids of revolution is entirely difficult or even impossible to calculate for that matter using the disk/washer method. Fortunately, this is another way to slice the problem (literally).
Any solid of revolution can be sliced into really thin cylindrical shells that fit snugly within each other. Then, each shell’s volume can be computed and added up in order to get the volume of the whole solid.
In some cases, the integral is a lot easier to set up actually by using an alternative method, called Shell Method, otherwise also known as the Cylinder or Cylindrical Shell method.
The formula for finding the volume of a solid of revolution using Shell Method is given by:
`V = 2pi int_a^b rf(r)dr`
Here, `r` is the radius from the centre of rotation for a “typical” shell.