Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two...

What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...

Partners use materials to wrap three-dimensional objects to determine the formula for surface area. The groups use an orange to calculate the amount of peel it takes to completely cover the fruit. Using manipulatives, individuals then...

Review the principles of scaling areas and draws a comparison to scaling volumes with a third dimensional measurement. The exercises continue with what happens to the volume if the dimensions are not multiplied by the same...

This resource was written for the younger math learner, but finding the volume of an irregular solid is also a problem for algebra and geometry students. Based on Archimedes’ Principle, one can calculate the volume of a stone by...

Model good modeling practices. Young mathematicians first learn about cross sections and solids of revolution. They then turn their attention to special right triangles and to the Laws of Sine and Cosine.