7adv.MATH.10.D | Texas Essential Knowledge and Skills (TEKS)

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relationshipvolumerectangular prismrectangular pyramidcongruent basesheightsformulas

model (the relationship between the volume of a rectangular prism and a rectangular pyramid with congruent bases and heights) #dok2
connect (the relationship between the volume of a rectangular prism and a rectangular pyramid to their formulas) #dok2
compare (the formulas and volumes of rectangular prisms and pyramids) #dok2
explain (the relationship between a prism's and pyramid's volume mathematically and visually) #dok3

I can use models to show how the volume of a rectangular prism relates to the volume of a rectangular pyramid with the same base and height. #dok2
I can connect the relationship between the volume of a rectangular prism and a rectangular pyramid to their formulas. #dok2
I can compare the volume formulas for rectangular prisms and rectangular pyramids and explain why the pyramid's volume formula has a 1/3 factor. #dok2
I can explain the reasoning, using models and calculations, for why a rectangular pyramid with the same base and height as a rectangular prism has 1/3 the volume. #dok3

Volume formulas for prisms and pyramids are connected through geometric relationships involving the base area and the height.
A rectangular pyramid with congruent base and height to a rectangular prism always has exactly one-third of the prism's volume.

How is the volume of a rectangular prism related to the volume of a rectangular pyramid with the same base and height?
Why does the formula for the volume of a pyramid include a factor of one-third?
How can models help demonstrate the relationship between prisms and pyramids?
What real-world objects can be used to illustrate the relationship between the volumes of prisms and pyramids?
How does understanding this relationship help when solving real-world problems involving volume?