Back to Describe the two-dimensional figures that result from slicing three-dimensional figures — Problem 2 · Task Set 25

7.G.A.3 Tutor Intake -- Cross-Sections of Prisms and Pyramids

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Grade 7·7 problems·~9 min·Common Core Math - Grade 7·standard·7-g-a-3

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Concepts

A rectangular pyramid is sliced with a horizontal cut close to
its apex, then with another horizontal cut close to its base.
Why do these two cuts produce cross-sections of DIFFERENT sizes?

Because the position of the cutting plane changes how much of the pyramid's width remains at that height.

They shouldn't be different sizes — all horizontal cuts of the same pyramid produce the same-sized cross-section.

Because horizontal cuts near the apex always produce triangles, while cuts near the base produce rectangles.

The size only depends on the pyramid's height, not on where along that height the cut is made.