HS Math Concept: Geometric Measurement and Dimension


Geometric Measurement and Dimension


Explain volume formulas and use them to solve problems.
HSG-GMD.A.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 information limit arguments. tools-icon
HSG-GMD.A.2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. tools-icon
HSG-GMD.A.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. tools-icon
Visualize relationships between two-dimensional and three-dimensional objects.
HSG-GMD.B.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. tools-icon
5. Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k2, and k3, respectively; determine length, area and volume measures using scale factors. CA  tools-icon
6. Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real world and mathematical problems. CA  tools-icon