3D Shapes and Their Properties

 

Common 3D Shapes and Their Properties

3D shapes are solid objects that have length, width, and depth. Each shape has unique faces, edges, and vertices.

Prisms

Definition: A prism is a 3D shape that has the same cross-section throughout its length.

• Cube: Square cross-section.

• Cuboid: Rectangular cross-section.

• Triangular Prism: Triangular cross-section.

• Hexagonal Prism: Hexagonal cross-section.

 

 

Properties of Prisms:

• Two identical parallel faces (bases).

• Other faces are rectangles.

 

Cylinders

Definition: A cylinder is similar to a prism but has a circular cross-section. 

 

 

Properties:

• Two circular faces.

• One curved surface.

• No vertices.

 

Pyramids

Definition: A pyramid has a flat base and triangular sides that meet at a single point.

• Triangular-based pyramid (Tetrahedron): 4 triangular faces.

• Square-based pyramid: 1 square base, 4 triangular faces.

• Rectangular-based pyramid: 1 rectangular base, 4 triangular faces.

 

 

Properties of Pyramids:

• The base determines the shape.

• The sloping faces are triangles.

 

Cones

Definition: A cone has a circular base and a curved surface that tapers to a point.

 

 

Properties:

• 1 circular base.

• 1 curved surface.

• 1 vertex at the tip.

 

Spheres

Definition: A sphere is a perfectly round 3D shape.

 

 

Properties:

• 1 curved surface.

• No edges or vertices.

 

Faces, Edges, and Vertices in 3D Shapes

Definitions:

• Face: A flat or curved surface of a 3D shape.

• Edge: A line where two faces meet.

• Vertex (plural: vertices): A point where edges meet.

 

Example: Cube

• Faces: 6 (all squares)

• Edges: 12

• Vertices: 8

 

Example: Cylinder

• Faces: 2 circular faces, 1 curved surface

• Edges: 2 (at the top and bottom)

• Vertices: 0

Nets of 3D Shapes

A net is a 2D pattern that can be folded to create a 3D shape.

Common Nets:

• Cube: 6 connected squares.

• Cuboid: 6 rectangles arranged in a cross shape.

• Cylinder: 2 circles + 1 rectangle.

• Pyramid: A base with attached triangles.

 

 

Example: Net of a Cube

A cube's net consists of 6 square faces arranged in a cross pattern.

 

Example: Net of a Cylinder

A cylinder's net consists of:

1. 2 circles (top and bottom faces)

2. 1 rectangle (curved surface laid flat)