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### Course: Geometry (FL B.E.S.T.)>Unit 9

Lesson 4: 2D vs. 3D objects

# Ways to cross-section a cube

Learn about all the different ways we can obtain cross-sections of a cube.

## Want to join the conversation?

• Am I the only one who finds this concept really confusing? Personally, I find it hard to visualize all the different cross-sections a particular 3D object has (not just in the context of a cube). Anyone have a trick to understand cross-sections better?
• If you have a real cube that you're willing to ruin with a marker, you can draw on it to help you understand the cross section better. If not, you can use a 3D online model program, such as Vectary. Alternatively, you can make cubes of jello and actually cut them so that you don't have to visualise it.
• can you get a regular pentagon?
• Mhm, a regular pentagon isn't possible.
Let me explain why.
If every side would be equal, you'd have to have sides which would at least have to be smaller than the hypotenuse or square's diagonal.

If the first cut would be smaller, you'd have to reach an asymmetrical point to get a pentagon which again would leave you with two distinct and unequal side lengths.

Another way to imagine this is a circle and a pentagon.
You'd have to have 5 equally distant points and this isn't achievable in a cube if you leave the center of symmetry, with a plane which only cuts quadrilaterals, namely the midpoint.
• Is there a methodical approach to slicing a 3D object to find if a particular 2D shape exists, or do you just have to brute force it?
• he says it at the end
you can slice 2D shapes with maximum as many sides as the cube has faces
• I didn't understand anything from this video...
• same here bro.
• What does opake mean? ()
• opaque means you can't see through it, for example, your hand is opaque because you can't see through it but glass isn't opaque because you can see through it.
• Is it possible to make a hyperbola, a circle, an ellipse, and a parabola with a cube?
• Not with a simple plane, which is where conic sections comes from, since all those are made by intersecting cones with planes.
• For some reason, I thought about the Tezarack from the villain Loki, Thor's brother. :/
Has anyone thought of that?
Sal is trying to find the infinity stone inside! :o
:) :D
• HIS DRAWINGS ARE SO NICE!!

Yeah it does look a bit like the Tesseract (the Cube)!! :)
• Too complicated?
• yes its too complicated.
• From time to time i come back to watch these 'cross-section a cube videos' and every time i don't understand them.! ugh!
• Okay this might help some people who are confused:

The places Sal sliced on the cube that resulted in a Pentagon and a Hexagon are different!

In the pentagon, he sliced it from the ONE OF SIDES of the cube! (Any face/side that IS NOT THE TOP FACE/BOT FACE)

In the hexagon, he sliced it from the TOP SIDE/FACE of the cube!

(Also, if you watch until the end of the video, Sal DOES say we're not cutting through the bottom side in the pentagon one. So It's REALLY IMPORTANT to watch these videos until the end, because you might miss a crucial piece of information that's necessary to piece everything together!)