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

recall the formula used to find the volume of a solid generated by revolving a region bounded by curves about a horizontal or vertical axis,
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 integration.

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Worksheet

Q1:

Which of the following has the volume represented by the integration ?

Q2:

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

Q3:

Find the volume of the solid generated by turning, through a complete revolution about the -axis, the region bounded by the curve and the lines , , and .