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Understanding the Shell Method for Calculating Volume of Solids of Revolution

The shell method is an effective technique for calculating the volume of solids of revolution, particularly when revolving around the y-axis. By taking vertical slices and imagining them as cylindrical shells, we sum the volume of these shells to find the total volume. The formula involves the product of circumference, height, and thickness. This section describes how to find the volume of a solid generated by rotating a function (f(x)) about the y-axis and discusses how to account for multiple functions when determining the volume of the region bounded by curves.

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Understanding the Shell Method for Calculating Volume of Solids of Revolution

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  1. Section 7-3 Volume using The Shell Method

  2. The shell method is like the washer method only the rotation is about the y-axis. http://www.rkm.com.au/animations/animation-solid-revolution-2.html

  3. If we take a vertical slice and revolve it about the y-axis we get cylinders. Then we add up the volume of all the cylinders

  4. Sum of the cylindrical shells Volume = ∑circumference ∙ height ∙thickness

  5. One Function: The volume of the solid obtained by revolving R about the y-axis using cylindrical shells is given by:

  6. 1. Find the volume of the solid obtained by revolving f(x) about the y-axis if

  7. Two Functions: The volume of the solid of revolution of the region bounded by f(x) and g(x) is given by:

  8. 2. Find the volume of the revolution of the region bounded by the curves

  9. 3. Find the volume of the solid of revolution bounded by • rotated about the y-axis

  10. Assignment • Practice 7-3 Shells • Reference http://www.msstate.edu/dept/abelc/math/volume.html

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