The Kid Should See This

Slicing Three Dimensional Figures

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Cylinders, cones, cubes, rectangular pyramids, polygons, right rectangular cones, right rectangular pyramids. When you slice through these three dimensional shapes, what two-dimensional shapes are revealed? It depends on how you slice it.

“If you cut through a cylinder with a geometric plane parallel to the cylinder’s base,” Planet Nutshell explains in the geometry video above, “the two-dimensional cross-section is a circle…”

slicing a cylinder across

“When you slice a cylinder from top to bottom that is perpendicular to its base, then look at the cross-section straight on, you get a rectangle. What happens when you slice a square pyramid?

“Remember you’re slicing a solid three-dimensional figure with a geometric plane. You can slice in any direction, just keep in mind that shapes can look different when you look at them from different angles, so orient the cross-section on the geometric plane.”

Cambridge, Massachusetts-based creative studio Planet Nutshell has an entire series of Math Shorts, produced in collaboration with Kentucky Educational Television, Utah Education Network, and WGBH Boston. Find their animated math videos in this playlist on YouTube.

β€’Β Teaching Tips for Slicing Three Dimensional Figures; Support Material for Teachers can be found at PBS Learning Media.
β€’Β Interactive: Cross Sections of a Cube from GBH.
β€’ Handout: Cross Sections of a Cube from GBH.
β€’ Recognizing common 3D shapes, a Khan Academy lesson.

Previously: How to find unknown angles.

Plus more geometry and math, including:
β€’ The Pythagorean theorem water demo
β€’ How do triangles help astronomers map the Milky Way?
β€’ How to draw a floating / levitating cube
β€’Β Why do honeybees love hexagons?
β€’ Topology, a 1961 Eames film for IBM’s Mathematica Exhibit
β€’ Symmetry, an Eames animated short for the 1961 Mathematica exhibition

Bonus: Balablok (1972) – Bretislav Pojar’s animated parody of human nature.

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