Basic 3D Shapes

A 3D shape, also called a solid shape, is a shape that has length, width, and height. Because it takes up space in three directions, you can pick it up, hold it, and turn it around. This is different from a 2D shape, which is flat and only has length and width. If you have already looked at the introduction to 2D shapes, basic 3D shapes are the natural next step: instead of flat outlines like squares and triangles, we now study solid objects like boxes and balls.

3D shapes are all around you. A soccer ball, a soup can, an ice cream cone, a tissue box, and a party hat are all everyday examples of basic 3D shapes.

To describe and compare 3D shapes, we use three key parts:

• Face: a flat or curved surface on the outside of the shape.
• Edge: a line segment where two faces meet.
• Vertex: a corner point where two or more edges meet (plural: vertices).

Look at the cube below. It has flat square faces, straight edges, and sharp corner vertices.

A cube has 6 flat faces, 12 straight edges, and 8 vertices. Some shapes, like a sphere, have no edges or vertices at all because their surface is completely curved. To dig deeper into how these three parts describe and classify every solid, see attributes of 3D shapes.

Here are the basic 3D shapes you will see most often, along with their key parts and a familiar real-world example.

Notice that the cube and the rectangular prism have the same number of faces, edges, and vertices. What makes them different is the size and shape of their faces: a cube's faces are all identical squares, while a rectangular prism can have faces of different rectangular sizes.

It helps to notice which basic 3D shapes are built from flat 2D shapes. A cube is made of square faces, a square pyramid is made of a square base and triangular faces, and a rectangular prism is made of rectangles. If you can already spot polygons and non-polygons, you can use that skill to describe the faces of a 3D shape. For a side-by-side look at how flat and solid shapes differ, check out comparing 2D and 3D shapes.

Question: A solid shape has 1 flat circular face, 1 curved face, 1 edge, and 1 vertex. What shape is it?

Solution: Compare these clues to the table above. Only the cone matches: it has a flat circular base, one curved surface that comes to a point, one edge where the flat and curved faces meet, and one vertex at the tip. So the shape is a cone.

You can check this kind of solid using the relationship \( F + V - E = 2 \). For the cone, \( 2 + 1 - 1 = 2 \), which matches, confirming the answer is consistent.

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