Three-Dimensional Shapes

In solid geometry, we study three-dimensional (3D) shapes, such as cubes, cylinders, and spheres. The diagrams below show some examples of these shapes.\(\quad\)\(\quad\) \(\quad\)

A surface is the outside of a three-dimensional (3D) shape. It is the part of the shape you can touch.

A face is a flat surface on a three-dimensional shape.

An edge is a straight line where two faces meet.

A vertex is a corner of a three-dimensional shape. It is a point where two or more edges meet.

This box-shaped solid has many faces, edges, and vertices. One example of each is shown.

When we draw 3D (three-dimensional) shapes on paper, we can only see the front of the shape. Some edges are behind and cannot be seen. These are called hidden edges. To show that an edge is hidden but still part of the shape, we draw it with dashed lines. Solid lines show the edges we can see.

We can sort three-dimensional (3D) shapes by counting their faces, edges, and vertices. Some examples are shown in the table below.

Name	Shape	Faces	Edges	Vertices
Cube		6 (flat faces)	12	8
Sphere		1 (curved surface)	0	0
Square Pyramid		5 (flat faces)	8	5
Cylinder		3 (1 curved, 2 flat faces)	0	0

Note: Shapes that have only curved surfaces, like the sphere and the cylinder, do not have edges or vertices.

A multi-view projection is a way to show a 3D shape using several 2D drawings. Each drawing shows how the shape looks from a different side, such as the front, the right side, or the top. These views help us understand the shape more clearly.

Draw the front, right, and top views of this solid.