One calculus project idea is figuring out the center of mass of an irregular piece of Plexiglas. Students choose a piece of Plexiglas and use coordinate paper to determine its boundaries. They use that information to determine the centroid of the region, proving it by balancing the Plexiglas on a pencil stuck in sand. Students turn in drawings and examples of the work they used to arrive at the answer.
Another calculus project is estimating the volume of water that runs through a creek. To do this, students create a cross section of the creek bottom. They take data measurements, including the length of time it takes a ping pong ball to travel 25 feet. This helps them arrive at the measurement for the area of the creek bottom. They use these measurements and calculus formulas to make their estimation.
Students can also use calculus to determine information about a wine glass. For this project, they use measurement and calculations to determine the following: the inner volume of the glass, the inner surface of the glass and the work needed to empty the glass using a pump.
Another option is calculating the design of an optimum gutter for a new office building. Students must design a gutter that removes the maximum amount of water. A given constraint is that only 12-inch wide gutter material may be used.