Students will work on an activity and asked to decide which of several objects do they think will roll the largest circle and why? In the main lesson they will work to produce a mathematical solution to Modeling Rolling Cups.
In this Khan Academy interactive, students use the formulas for cylinders, pyramids, cones and spheres to solve problems.
Surface Area and Volume of spheres worksheet.
In this task students examine another solid of revolution—a frustum—and create a strategy for finding its volume. They then use a variety of strategies to decompose a figure that consists of curved edges into cylinders, frustums and cones to generate a sequence of better and better approximations of the actual volume of the solid.
Students will work through a self-paced tutorial to learn some of the basics of Sketchup and produce a 3D design of a dog house incorporating their choices for materials and design. (Note: I have a collection of these tutorials that I am willing to share that build on student knowledge of Sketchup and introduce 1-2 new tools with each tutorial. This is just one of those tutorials.)
This video uses volume of a rectangular prism to solve a word problem.
Use an aerial photograph to determine the volume of the Great Pyramid of Giza.
This task provides an opportunity for students to solidify their understanding of solids of revolution in a problem-solving, modeling context. Students will decompose a geometric solid of revolution into familiar three-dimensional objects whose volumes can be calculated. Students will also need to draw upon their ability to reason with units when solving problems.
