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Mathematics » High School: Geometry » Geometric Measurement & Dimension

Standards in this domain:

• G-GMD.1
• G-GMD.2
• G-GMD.3
• G-GMD.4

Explain volume formulas and use them to solve problems

• G-GMD.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.
• G-GMD.2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
• G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.^★

Visualize relationships between two-dimensional and three-dimensional objects

• G-GMD.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.