Gizmo of the Week: Surface and Lateral Areas of Prisms and Cylinders

Students can channel the artist Christo through the Surface and Lateral Areas of Prisms and Cylinders Gizmo. Christo is an artist devoted to a very particular form of artwork—wrapping (or surrounding) large objects in fabric. Along with his wife Jeanne-Claude, the couple has wrapped the Pont Neuf in Paris; Berlin’s Reichstag building; trees in Basel, Switzerland; and a chunk of the Australian coast near Sydney. Their projects involved millions of square meters of fabric, as well as precise calculations of the area of fabric needed for each project.

In the Gizmo, students learn how to simplify 3D surface area problems into a series of 2D problems. After introducing students to a real-world problem involving wrapping
paper, the Gizmo lesson continues with a step-by-step explanation of how “flattening” a shape into a net changes a 3D figure into a combination of simple 2D shapes. Throughout the lesson, students are asked to make generalized expressions that lead to a derived formula. At the end of the Gizmo, students are equipped to describe in their own words the process of computing surface areas of these shapes.

For students who are ready for more challenging 3D shapes, the Surface and Lateral Area of Pyramids and Cones Gizmo continues this lesson. If you are interested in the art of Christo and Jeanne-Claude, visit their page.