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## Get ready for AP® Calculus

### Course: Get ready for AP® Calculus>Unit 7

Lesson 7: 2D vs. 3D objects

# Rotating 2D shapes in 3D

If you rotate a 2D shape about an axis, the shape will define a 3D object. Watch Sal rotating various 2D shapes and see what 3D objects he gets!

## Want to join the conversation?

• How are you supposed how to do half-spheres and rectangles when he never showed us? I cannot get the practice problems. Does anyone have any tips on how to figure it out?
• Cut out the shape from a piece of paper and tape it to a toothpick (or pencil). Roll the toothpick between your hands so it spins quickly. As it moves, what shape do you see?
• How does something 2D become 3D?
• By rotating it around an axis, not a point. The best way I can think about it is to talk about a magazine. While it is not 2D, when it is closed, it is flat and fairly skinny. But if I open it up and put the front and back cover together, and try to fan out the pages as much as possible, it becomes much more of a 3D object sort of in the shape of a cylinder. Thus, my rotation would be around the spine of the magazine.
Hope this helps.
• Why does Sal sound depressed in this video, compared to the previous and future videos? Is everything ok?
• :48
Is rotation when you flip it or reflection?
• Rotation, his goal is to turn it 3 dimensions, not to reflect it. Hope this helps! 😊
• What solid figure can have the same cross section as a sphere
• A cylinder or a cone, assuming the cross-section is parallel to the base.
• i dont understand How something 2D becomes 3D?
• It is not exactly changing a 2d object into a 3d object, it is more related to rotating a circle and putting billions and billions of these circles together to form a sphere. This would be like taking a magazine (not quite 2D, but pretty flat and thin compared to the lengths and widths. However, people fold each page and glue the front cover to the back cover to create a tree or some other 3D figure.
• My question show me a triangle and says that its either a cone or cylinder by 1 unit of the/ Line m? is it possible that my answer is going to be a cylinder?
• no you cannot cross-section a cylinder to get a triangle, but a cone can be cut parallel to the base through the vertex to get a triangle.
• if its a rectangle how do i start to rotating the shape?
• Think of what pattern the endpoints will make (just like the leg of the triangle would create a circle when rotated, but the point would not move. Both ends would form congruent circles, thus creating a cylinder. So what would happen if you have a magazine and you opened it so that the front and back cover are touching? You would see each of the pages on top and bottom would be on a two congruent circles.