The shell method is a mathematical technique used to find the volume of a solid of revolution by integrating the product of the circumference of a shell and its height.
The shell method is based on the circumference of a shell, while the disk method uses the radius of a disk. Additionally, the shell method is used when the axis of revolution is parallel to the axis of integration, while the disk method is used when the axis of revolution is perpendicular to the axis of integration.
The formula for the shell method is V = 2π ∫(radius)(height)(thickness) dx, where the radius is the distance from the axis of revolution to the shell, the height is the function of x, and the thickness is the width of the shell.
No, the shell method can only be used for finding the volume of solids of revolution that have a cylindrical shape, such as a cone, a cylinder, or a frustum (truncated cone).
You can check if you have set up the shell method correctly by making sure that the axis of revolution is parallel to the axis of integration, and that the height and thickness of the shell are correctly defined in terms of the variable of integration. You can also check your answer by using a different method, such as the disk method, to see if you get the same result.