Problem 1 explores the relationship between height and volume of a right cylinder, the height and surface area, and the surface area and volume with a set radius measure.

Problem 2 explores the relationship between the radius and volume, radius and surface area, and surface area and volume when the height is kept stable.

Transfer the file PaintCan.tns to students' handhelds before starting the activity. Students will begin with the Paint Can Dimensions worksheet and the PaintCan.tns file.

They should be familiar with the basic features of the TI-Nspire such as how to open a file, grab and move objects, enter a function into the Graphs & Geometry application, and how to adjust the window setting manually.

This activity is designed to be student-centered - the teacher may act as a facilitator while students work cooperatively to help them with the handheld.

This activity can be used to introduce algebraic modeling or as a review lesson. A challenge question is posed to further work on algebraic manipulation of a formula.

Problem 1 explores the relationship between height and volume of a right cylinder, the height and surface area, and the surface area and volume with a set radius measure.

Problem 2 explores the relationship between the radius and volume, radius and surface area, and surface area and volume when the height is kept stable. Questions are posed that encourage integration between geometric formulas and algebraic modeling. Students are asked to compare and explore these measures through the interactive functionality of numerical and graphical representations.

The PaintCan_Soln.tns file shows expected results.