Solids Whose Cross Sections Have the Same Shape

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Creating areas based on the integration of heights and volumes based on the integration of areas are important concepts in calculus. Students are often asked to determine the volume of a solid, the base of which is the intersection of two curves. The cross sections of the solid perpendicular to the axis all have the same shape, with some important dimension of that shape determined by the two curves. Here are a few examples of what these solids would look like for the intersection of the curves , and . This can help students visualize the solid in question.

Contributed by: Glenn Beatty and Mark Evans (Science and Mathematics Academy) (March 2011)
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.