How to Find Volumes of Revolution With Integration


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question 1 of 3

What is the equation for the volume enclosed by revolving f(x) around the x axis between x=a and x=b?

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1. What is the equation for the volume enclosed by revolving the area between f(x) and g(x) (where f(x) < g(x)) around the x axis between x=a and x=b?

2. What is the volume made by revolving f(x) around the x-axis between x=0 and x=1?

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About This Quiz & Worksheet

To find the volume of revolutions with integration, you will need to understand how to use the volume of revolution integration technique, and this quiz and worksheet combo will help you test yourself on this technique. These practice questions will test you on identifying appropriate equations to use in certain situations and your ability to find the volume of a given function made by revolving around an axis.

Quiz & Worksheet Goals

In these assessments, you'll be tested on:

  • Your ability to determine the appropriate equation to use given certain information about a function
  • Identifying the volume made by revolution around an axis

Skills Practiced

This quiz and worksheet will allow you to test your skills in the following areas:

  • Reading comprehension - ensure that you draw the most important information on the relevant equations, volumes of revolution, and using integration from the related lesson
  • Problem solving - use your acquired knowledge to solve practice problems involving the identification of volumes of revolution
  • Information recall - use your knowledge to answer questions about finding volumes of revolution with integration

Additional Learning

To learn more about this topic, review the accompanying lesson on finding volumes of revolutions with integration. This lesson covers the following objectives:

  • Define generating regions
  • Define and understand the Slicing Method
  • Define and understand the Disk Method
  • Define and understand the Washer Method
  • Understand how to find the volume of a revolution using integration