G-GMD: Geometric Measurement and Dimension

Geometric Measurement and Dimension

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Geometric Measurement and Dimension covers volume formulas for cylinders, pyramids, cones, and spheres, with informal justifications using Cavalieri's principle. Cross-sections of three-dimensional figures and solids of revolution connect two- and three-dimensional geometry. The work builds fluency in applying formulas while developing spatial reasoning about three-dimensional shapes.

G-GMD.1Explain how to find the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.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.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. For example: Solve problems requiring determination of a dimension not given.G-GMD.4Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Example Problems
Find the area of a circle with a radius of .
Either enter an exact answer in terms of
or use for and enter your answer as a decimal.
A hexagonal pyramid has a volume of and a height of .
What is the area of the base of the pyramid?
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