Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

## Solids of Revolution

#### Activity Overview

Students will investigate 3D visualizations of volumes created by rotating a function about the x-or y-axis. They will understand the concept and reason for the volume formula in order to be prepared for generalizations. Students will solve the definite integral by hand using the fundamental theorem of calculus and using the definite integral capabilities of the TI-Nspire. They will compare their solution with the volume of a cone that would be the same as or approximate the shape.

#### Key Steps

• Page 2.7 shows an equation being rotated about the y-axis to form a parabaloid.  Students can then explore through manipulation of variables to see the relationships.