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Cavalieri's Principle in 2D
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Cavalieri's Principle in 2D

Geometry & Algebra II Archive

Geo U5: Extending to Three Dimensions

Big Idea: Big Idea 1

Geogebra slider that represents the area of a rectangle split horizontally to represent Cavalieri's Principle in 2D.

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Geometry: Extending to Three Dimensions
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cavalieri's principle
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Comparing Perimeter, Area, and Volume
Resource:
Comparing Perimeter, Area, and Volume

Geometry & Algebra II Archive

Geo U5: Extending to Three Dimensions

Big Idea: Big Idea 1

These three parts are intended to support students in making connections between 2 dimensional and 3 dimensional objects, especially how scaling changes these objects and how we can carefully partition objects in order to make relationships between two otherwise different geometric shapes.

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Type
Geometry: Extending to Three Dimensions
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Tags
cavalieri's principle, perimeter, similarity, surface area, volume
Standards
Common Core: Major Standards ( G-MG.A.1, G-MG.A.3 ) Common Core: Additional Sta…
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Common Core: Major Standards:
G-MG.A.1

Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

G-MG.A.3

Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★

Common Core: Additional Standards:
G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

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