Mathematics » High School: Geometry » Geometric Measurement & Dimension

Explain volume formulas and use them to solve problems

• 1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

  Suggested tag: cc-9-12m-g-gmd-1

• 2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

  Suggested tag: cc-9-12m-g-gmd-2

• 3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.^★

  Suggested tag: cc-9-12m-g-gmd-3

Visualize relationships between two-dimensional and three-dimensional objects

• 4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

  Suggested tag: cc-9-12m-g-gmd-4