Shell Method
The Shell Method is a technique used in calculus to find the volume of a solid of revolution. It involves slicing the solid into cylindrical shells, which are then integrated to calculate the total volume. This method is particularly useful when the solid is generated by rotating a region around an axis that is not one of the boundaries of the region.
To apply the Shell Method, you typically identify the height and radius of each shell based on the function being rotated. The volume of each shell is calculated using the formula V = 2\pi \times \textradius \times \textheight \times \textthickness . The total volume is found by integrating this expression over the interval of interest, often involving functions like f(x) or g(y).