7.7 Volume Washer Methodap Calculus

This method is known as Cylindrical Shells or the Shell Method.

Kuta Software - Infinite Calculus Name Volumes of Revolution - Washers and Disks Date Period For each problem, find the volume of the solid that results when the region enclosed by the curves is revolved about the the x-axis. 1) y = −x2 + 1 y = 0 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8. AP Calculus 605 Volume of Revolution with Disk, Washer and Shell methods! AP Calculus 605 Volume of Revolution with Disk, Washer and Shell methods! Unit 7 Notes 7.7 Volume Washer Hw 7.7 Volume Washer. Powered by Create your own unique website with customizable templates.

In our previous lecture, we discussed the disk and washer method and came up with just one formula to handle all types of cases.

In this lesson, we will use the Calculus Shell Method to find the volume of a solid of revolution. But, we use this method for specific cases when we cannot use the disk and washer method.

7.7 volume washer method ap calculus solver

The formula for the Shell Method comes from the idea that we are going to take a bounded region and spin or revolve infinitely thin cylinders about an axis or line.

To generate the formula, we have to remember how to find circumference, area, and volume.

This method differs from the Disk & Washer method which uses rings. Now we can use any shape for the cross-section with one caveat. The shape must be able to expand or contract to cover the solid we’re evaluating, as stated in Paul’s Online Notes.

Moreover, compared to the Disk & Washer Method this method has a significant distinction.

For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.

Just look at it graphically in the detailed diagrams below:

In the video lesson below, we will walk through three classic examples. These examples provide a solid understanding of how and when to use this shell method.

Solids of Revolution – Shell Method Video

Solids of Revolution – Shell Method – 3 Examples


Shell Method Examples

7.7 Volume Washer Method Ap Calculus Notes

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