Volume by rings, also known as volume by disks or volume by washers (if the area between two functions is being rotated around an axis), is a method of finding the volume of a solid of revolution. This method involves splitting the shape into indefinitely small circular rings. The formula for the volume of any solid of rotation is or , depending on which axis the rotation is around. In the case of volume by rings, the formula is
assuming the rotation is around the x-axis. If the rotation is of an area between two functions, the formula is
To find the volume of the resulting solid when is rotated around the -axis on the interval , substitute into the formula.
This method can also be used to find the formula for the volume of shapes. Take for example the formula for the volume of a sphere, . A sphere is a graph of rotated around an axis (here we will assume it is the -axis). Begin by isolated . It is important to keep in mind that is not a variable and must not be treated as one.