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Miss Battaglia AP Calculus

7-3 Volume: The Shell Method Objective: Find the volume of a solid of revolution using the Shell method. Compare to the disk method. Miss Battaglia AP Calculus. The Shell Method. Alternative to finding volume of a solid of revolution.

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Miss Battaglia AP Calculus

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  1. 7-3 Volume: The Shell MethodObjective: Find the volume of a solid of revolution using the Shell method. Compare to the disk method. Miss Battaglia AP Calculus

  2. The Shell Method • Alternative to finding volume of a solid of revolution. • Called the shell method because it uses cylindrical shells.

  3. The Shell Method To find the volume of a solid of revolution with the shell method, use of the following Horizontal Axis of RevolutionVertical Axis of Revolution

  4. Using the Shell Method to Find Volume Find the volume of the solid of revolution formed by revolving the region bounded by y=x-x3 and the x-axis (0<x<1) about the y-axis.

  5. Using the Shell Method to Find Volume Find the volume of the solid of revolution formed by revolving the region bounded by the graph of and the y-axis (0<y<1) about the x-axis.

  6. Comparison of Disk and Shell Methods Disk method: representative rectangle is always perpendicular to the axis of revolution. Shell method: representative rectangle is always parallel to the axis of revolution.

  7. Shell Method More Preferable Find the volume of the solid formed by revolving the region bounded by the graph of y=x2+1, y=0, x=0, and x=1 about the y-axis.

  8. Volume of a Pontoon A pontoon is to be made in the shape shown in the figure ***ADD FIGURE. The pontoon is designed by rotating the graph of

  9. Shell Method Necessary Find the volume of a solid formed by revolving the region bounded by the graphs of y=x3+x+1, y=1, x=1 about the line x=2.

  10. Classwork/Homework

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