About Shell Method Formula
Decomposing a solid of revolution in cylindrical shells is used to find the volume using the Shell Method. We generate the shells by slicing the solid parallel to the axis of revolution. The surface area of cylinder and the thickness of the cylindrical wall is used to calculate the volume of the cylindrical shell.
Let R denote the area bordered by x=a and x=b. Let's say we want to make a solid by rotating it around a vertical axis. Let r(x) be the distance between the rotation axis and x, and h(x) be the height of the shell.
Volume of the solid is given by
The volume of solid obtained by revolving it around the y-axis the region under y = f(x) from a to b is
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