Volumes of solids with known cross-sections - Integration Applications

You’re one step closer to a better grade.

Learn with less effort by getting unlimited access, progress tracking and more.

Learn More

Volumes of solids with known cross-sections

In this section, we learn that cross sections are shapes we get from cutting straight through the curve. We want to find the area of that cross section, and then integrate it with known bounds to find the volume of the solid. In most cases they will tell you what the shape of the cross-section is, so that you can find the area of cross-sections immediately.


Cross-Section Area of Solid = A(x)
volume of solid formula

derive volume of a solid with the cross-section shape given
Teacher pug

Volumes of solids with known cross-sections

Don't just watch, practice makes perfect.

We have over 350 practice questions in Calculus for you to master.

Become a Member to Get More!

  • Easily See Your Progress

    We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

  • Make Use of Our Learning Aids

    Last Viewed
    Practice Accuracy
    Suggested Tasks

    Get quick access to the topic you're currently learning.

    See how well your practice sessions are going over time.

    Stay on track with our daily recommendations.

  • Earn Achievements as You Learn

    Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

  • Create and Customize Your Avatar

    Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.