Activity Overview
Use visual representation of solids of revolution to find the exact volume of the solid.
Objectives
- Visualize a solid generated by revolving a graph about the x-axis
- Calculate the area of a cross section of a solid generated by rotating a function graph about the x-axis
- Use the area of a cross section of a solid generated by rotating a function graph about the x-axis to estimate and find the exact volume of the solid
Vocabulary
- revolve about the x-axis
- solid
- disk
About the Lesson
This lesson involves giving students a visual representation of solids of revolution. As a result, students will:
- Observe that the solid generated by revolving the function graph about the x-axis can be generated by disks centered on the x-axis, the radius of which correspond to the value of the function at that point.
- Observe that the volume of a solid of revolution can be estimated using a sum of volumes of disk slices.
- Observe that exact volume can be found using integration.
NOTE: While this TI-Nspire document provides an aid in visualizing a solid of revolution, it is a good idea to have a physical example for students to consider, such as a vase or lamp or a table leg that has been shaped on a lathe or a ceramic piece shaped on a pottery wheel.