Lesson: Volumes of Solids of Revolution Mathematics • Higher Education

In this lesson, we will learn how to find the volume of a solid generated by revolving a region around either a horizontal or a vertical line using integration.

Lesson Plan

Students will be able to

understand how we derive the disk and washer methods,
find the integral used to calculate the volume of a solid generated by revolving a region bounded by given curves about a horizontal or vertical axis,
find the volume of a solid formed by rotating a region bounded by curves using the washer method.

Lesson Video

Lesson Explainer

Sample Question Videos

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02:45
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Lesson Worksheet

Q1:

Consider the region bounded by the curves , , , and . Determine the volume of the solid of revolution created by rotating this region about the -axis.

Q2:

Find the volume of the solid obtained by rotating the region bounded by the curve and the lines and about the -axis.

Q3:

Consider the region bounded by the curve and the lines , , and . Set up an integral for the volume of the solid obtained by rotating this region about the -axis.