Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
The slicing method is a technique used to determine the volume of a solid by integrating the cross-sectional area perpendicular to an axis. It involves summing up infinitesimally thin slices of the solid.
5 Must Know Facts For Your Next Test
The integral setup for the slicing method generally takes the form $V = \int_a^b A(x) \, dx$, where $A(x)$ is the cross-sectional area at position $x$.
The cross-sectional area function $A(x)$ must be determined based on the geometry of the solid.
Slices are perpendicular to the axis along which you integrate, typically either the x-axis or y-axis.
In cylindrical coordinates, this method can be adapted to integrate with respect to $r$ and $\theta$ for solids of revolution.
Common shapes for slicing include disks, washers, and rectangular strips.
Review Questions
Related terms
Disks: Slices that are circular in shape; used when finding volumes by rotating a region around an axis.
Washers: Slices with a hole in them (ring-shaped); used when finding volumes by rotating around an axis but there is a gap between the region and axis.
Cross-Sectional Area: The area of a slice perpendicular to an axis, denoted as $A(x)$ or $A(y)$ depending on integration variable.