Three-Dimensional Shapes

Solid geometry studies three-dimensional shapes, such as cubes, cylinders, and spheres. The diagrams show examples of these shapes.\(\quad\)\(\quad\) \(\quad\)

A surface is the exterior of a three-dimensional shape.

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

An edge is a line segment where two faces meet.

A vertex is a point where two or more edges meet.

A polyhedron is is a three-dimensional shape with polygonal flat faces.

A cross section of a solid is a flat shape created when a plane cuts through the solid.

A uniform cross section means the cross section of a solid has the same size and shape at every point along its length.

Does this solid have a uniform cross section?

A prism is a polyhedron with a uniform cross section that is a polygon. Prisms are named according to the shape of their base.

Name	Figure	Cross Section
Triangular prism
Rectangular prism

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

When drawing 3D shapes, some edges are hidden because they are at the back of the shape. We call these hidden edges. To show the shape clearly, we use dotted lines for hidden edges. This helps us see the shape and its depth.

A multi-view projection is a way to draw a 3D shape using 2D views. You show how the shape looks from different sides, like the front, right, and top, to help understand its form.

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

A net is a flat 2D shape that can be folded along its edges to form a 3D solid. Dashed lines show where to fold.