Volumes by Cylindrical Shells

Shells sometimes work better than washers. The AP Calculus video presents an example of finding the volume of a rotational solid by using the shell method. The method uses the integral of the lateral surface area of a cylinder as opposed to the area of a washer.

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Instructional Ideas
  • Provide instruction on the integral formula to find the volume using shells
  • Work less complex problems before using the one in the video
Classroom Considerations
  • Individuals need to know how to find the approximate roots for a quadratic formula
  • The video presents a sketch of the graph to better understand the region
  • Reiterates how to find the dimensions needed for the integral
  • None