Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
A cross-section is the shape obtained by cutting a solid object with a plane. It is used to determine the volume of solids by integrating the areas of these cross-sections along an axis.
5 Must Know Facts For Your Next Test
Cross-sections are typically taken perpendicular to an axis, such as the x-axis or y-axis.
The area of each cross-section can be expressed as a function of the position along the axis (e.g., A(x)).
To find the volume of a solid using cross-sections, integrate the area function over the interval defining the solid.
Common shapes for cross-sections include circles, rectangles, and triangles.
In problems involving volumes by slicing, it's essential to correctly identify and set up the limits of integration.
Review Questions
Related terms
Volume: The amount of space occupied by a three-dimensional object, often found using integration in calculus.
A mathematical concept that computes the accumulation of quantities, such as areas under curves or total volumes.
Slicing Method: \text{A technique for finding volumes where a solid is divided into thin slices, and their combined volume is found through integration.}