For this project, students create a station.. They are assigned a 3D figure (cylinder, cone, prisms, pyramids, sphere, etc). They must create a station that teaches the parts of the figure and how to find the surface area, lateral area, and volume of the figure. Then students visit each station created and have a quiz on all the stations.

For this project, students create a station.. They are assigned a 3D figure (cylinder, cone, prisms, pyramids, sphere, etc). They must create a station that teaches the parts of the figure and how to find the surface area, lateral area, and volume of the figure. Then students visit each station created and have a quiz on all the stations.

In this activity, learners explore scale by using building cubes to see how changing the length, width, and height of a three-dimensional object affects its surface area and its volume. Learners build bigger and bigger cubes to understand these scaling relationships.

Challenged with a hypothetical engineering work situation in which they need to figure out the volume and surface area of a nuclear power plant’s cooling tower (a hyperbolic shape), students learn to calculate the volume of complex solids that can be classified as solids of revolution or solids with known cross sections. These objects of complex shape defy standard procedures to compute volumes. Even calculus techniques depend on the ability to perform multiple measurements of the objects or find functional descriptions of their edges. During both guided and independent practice, students use (free GeoGebra) geometry software, a photograph of the object, a known dimension of it, a spreadsheet application and integral calculus techniques to calculate the volume of complex shape solids within a margin of error of less than 5%—an approach that can be used to compute the volumes of big or small objects. This activity is suitable for the end of the second semester of AP Calculus classes, serving as a major grade for the last six-week period, with students’ project results presentation grades used as the second semester final test.