Volumes of Solids

  • Area is only one of the many applications of the definite integral.
  • Another important application is its use in finding the volume of a three-dimensional solid.
    • This section involves particular types of three-dimensional solid—one whose cross sections are similar.
  • Solids of revolution and volume by known cross section are used commonly in engineering and manufacturing.

Essential Questions

How can the volume of a solid be found using integration?

Skills

  1. Find the volume of a solid of revolution using the disk method.
  2. Find the volume of a solid of revolution using the washer method.
  3. Find the volume of a solid with known cross sections.