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Calculus: Visualizing Solids of Revolution - Washers

by Texas Instruments

Objectives

  • Visualize the solid generated by revolving the region bounded between two function graphs and the vertical lines x = a and x = b about the x-axis
  • Calculate the area of a cross section of a solid generated by rotating the region bounded between two function graphs and the vertical lines x = a and x = b about the x-axis
  • Use the area of a cross section of a solid generated by rotating a region bounded by two function graphs about the x-axis to find the exact volume of the solid

Vocabulary

  • revolve about the x-axis
  • solid
  • washer

About the Lesson

The intent of this lesson is to provide students with visual representations of solids of revolution. As a result, students will:

  • Observe that the solid generated by revolving the region bounded between two functions about the x-axis has cross sections shaped like washers centered on the x-axis, the radii of which correspond to the values of the upper function and the lower function at that point.
  • Observe that the volume of a solid of revolution can be estimated using a sum of volumes of washer slices.
  • Observe that the exact volume can be found by integration.

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