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Math 104: Calculus13 chapters | 104 lessons

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Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught Math at a public charter high school.

What's the difference between 2D and 3D shapes? Learn the answer to this question in this lesson. You will also explore what makes spheres and cubes 3D shapes.

We also recommend watching How to Calculate the Volumes of Basic Shapes and Finding Distance with the Pythagorean Theorem

What makes something 3D? Is it the way it looks? An easy way to think of a **3D shape** is any shape or object that takes up air space. Think about your own body for a minute. Your body is a 3D shape. It is not a uniform shape like a building block, but it is a 3D shape, nonetheless. What makes your body a 3D shape? Does it take up air space? Of course it does; you can't be at the same spot as anyone else. You can't take up the same space as a chair or a dog or anything else. Only you can occupy your space. This is what makes a shape 3D.

A test you can do to check whether something is 3D or not is to try to place something in the exact spot where that shape is. Look around you for something you can grab. Take your pen, for instance. Place it on your desk. Now, try and take another pen and place it in the same exact spot as your first pen. Can you do it? No, you can't. The only way you can do it is if you moved your first pen to make room for the second.

Even a flat piece of paper is a 3D shape in the world. Lay two pieces down, one on top of the other, and look at them. Are both sheets of paper taking up the same space? It may seem so at first, but look carefully. One is actually on top of the other because both take up space.

In mathematical terms, a 3D shape has three dimensions. The 'D' in '3D' stands for 'dimensional.' In a world with three dimensions, you can travel forwards, backwards, right, left, and even up and down. The ability to travel up into space and back down differentiates 3D from 2D. The world you live in is all 3D. You can walk anywhere on land and you can fly anywhere in the air. Underwater, you can swim in all three dimensions.

In mathematics, you have your standard 3D shapes that you need to know. These are shapes such as cylinders, spheres, cubes, and pyramids. These are all examples of 3D shapes.

What makes these shapes 3D? All four of the shapes take up space. A cylinder is the same shape as a soda can. You can't put two soda cans in the same space. The same thing goes for the sphere, which is a ball. You can't have two balls taking up the same space. One ball or sphere has to roll somewhere else. A cube is the same shape as a rolling dice you use in games. When you have two dice, you can only place them side by side. You can't squish them into the same space. The same goes for the pyramid. You can't have two pyramids in the same space. The pyramids in Egypt, for example, each take up their own distinct space.

Here's a partial list of some 3D shapes:

3D Shapes |
---|

Sphere |

Cube |

Cuboid (like a brick) |

Triangular prism |

Rectangular prism |

Cone |

Octahedron |

Dodecahedron |

Tetrahedron |

Cylinder |

Pyramid |

The world is 3D. Look around - whatever you can touch is a 3D shape. 3D shapes take up space. Only the 3D shape or object itself can occupy its own space. For example, no other human can stand where you are standing. In mathematics, there are standard 3D shapes such as spheres, cubes, prisms, cones, and pyramids.

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