Shell Method: Formula & Examples


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question 1 of 3

Let R be the region below y = x^3 and above the x-axis between x = 2 and x = 4. Let S be the solid of revolutions obtained by rotating R around the y-axis. Choose the integral that correctly computes the volume of S.

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1. A paraboloid is the solid of revolution obtained by rotating the region bounded by a parabola and the y-axis around the y-axis. Use the shell method to find the volume of the paraboloid formed from y = x^2 as it is rotated around the y-axis, between y = 0 and y = 9.

2. Find the volume of the solid of revolution obtained as the region of the first quadrant bounded by the line x = 3 - 2y is rotated around the x-axis.

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About This Quiz & Worksheet

The worksheet and quiz are effective tools when it comes to checking your knowledge of the shell method. You will be quizzed on formulas and examples of this method.

Quiz & Worksheet Goals

The quiz/worksheet combo can assess your understanding of:

  • Choosing integrals
  • Using the shell method
  • Finding the volume of a solid revolution

Skills Practiced

  • Problem solving - use acquired knowledge to find integrals and volumes
  • Information recall - access the knowledge you have gained regarding how to choose integrals correctly
  • Knowledge application - use your knowledge to identify how to use the shell method

Additional Learning

Develop your ability to use this method even more by reading the lesson, Shell Method: Formula & Examples. In this lesson, you'll get to cover these topics as well:

  • Computing the solid of revolution
  • Understanding the shell method formula
  • Using this method with different examples