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Understanding the Shell Method for Finding the Volume of Solids of Revolution

In this lesson, we explore the Shell Method, an essential technique for calculating the volume of solids formed by rotating a region around an axis. We focus on how to apply the Shell Method for both vertical and horizontal axes of revolution. The key distinction in this method is that our rectangles are oriented parallel to the axis of revolution. Students will learn to compute the volume of solids generated by revolving areas around the y-axis and the x-axis, deepening their understanding of volumetric geometry in calculus.

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Understanding the Shell Method for Finding the Volume of Solids of Revolution

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  1. AP Calculus AB Day 8 Section 7.3 Perkins

  2. Shell Method (for finding the volume of a solid of revolution) Most important difference is that our rectangles are chosen to be parallel to the axis of revolution! Vertical axis of revolution Horizontal axis of revolution

  3. 1. Use the shell method to find the volume of the solid generated by revolving the area enclosed by over about the y-axis. Shell Method:

  4. 2. Use the shell method to find the volume of the solid generated by revolving the area enclosed by over about the x-axis. Shell Method:

  5. AP Calculus AB Day 8 Section 7.3 Perkins

  6. Shell Method (for finding the volume of a solid of revolution) Vertical axis of revolution Horizontal axis of revolution

  7. 1. Use the shell method to find the volume of the solid generated by revolving the area enclosed by over about the y-axis.

  8. 2. Use the shell method to find the volume of the solid generated by revolving the area enclosed by over about the x-axis.

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