Expressing Geometric Properties with Equations

High School: Geometry » Geometric Measurement & Dimension #

Standards in this domain: #

Explain volume formulas and use them to solve problems #

CCSS.Math.Content.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 informal limit arguments.

CCSS.Math.Content.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.

CCSS.Math.Content.HSG.GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Visualize relationships between two-dimensional and three-dimensional objects #

CCSS.Math.Content.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.

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