Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Definite Integrals and Applications

9-12

45 Minutes

• ##### Device
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

## Visualizing Solids of Revolution - Washers

#### Activity Overview

Use visual representation of solids of revolution to find the exact volume of the solid.

#### 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

• solid
• washer

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.