Lesson: Volumes of Solids of Revolution Using the Shell Method Mathematics

In this lesson, we will learn how to find the volume of a solid generated by revolving an area around a vertical or horizontal axis using the shell method.

Lesson Plan

Students will be able to

recognize when it will be easier to find a volume using the shell method (integration is performed perpendicular to the axis of revolution) compared to the disk method (integration is performed parallel to the axis of revolution),
find the volume of a solid generated by revolving an area around a vertical or horizontal axis using the shell method.

Lesson Worksheet

Q1:

Calculate the volume of a solid generated by rotating the region bounded by the curve and straight lines and a complete revolution about the -axis.

Q2:

Calculate the volume of a solid generated by rotating the region bounded by the curve , the -axis, and the straight line a complete revolution about the -axis.

Q3:

Determine the volume of the solid generated by rotating the region bounded by the curve and the line a complete revolution about the -axis.