There are four types of volumes of revolution which are: the disk method,
washer method, shell method, and volume by cross section. Each of these volume
methods come in the form of integral, and they all require bounds. These
methods have a specific formula that can be followed. Volume of revolution
usually give one or more functions bounded by other functions or lines, and it is
asked to find the volume of that region by rotating it around some other line.
The disk method usually only consists of one function revolved around
either the x axis or the y axis. If the function is set equal to y, then the bounds
must be in terms of x’s otherwise it is the opposite which is in terms of y’s.
For
the disk method, there is a specific formula that can be followed which is the
integral of pi(r^2). The distance between the line that the region is revolving
around and the region is known as the radius. In all the formulas, it will be