In the past you have used the formulas for the volume of cylinders, pyramids, cones, and spheres. Here, you will derive those formulas using Cavalieri's principle. You will also solve many different types of problems that utilize your knowledge of three dimensions including modeling problems, density problems, and design problems.
You learned that the formulas for the volume of cylinders, pyramids, cones, and spheres can all be derived using Cavalieri's principle. You also learned that two dimensional shapes and three dimensional objects are connected in many ways. Three dimensional objects have two dimensional cross sections. Also, two dimensional shapes can be rotated around lines to create three dimensional objects.
You practiced modeling in three dimensions by choosing solids that best approximated real life objects and using your geometry knowledge about the solids to answer questions about the objects. You also explored density and design problems that were related to solids.