What are 3D Shapes?
In Geometry, 3D shapes, or three-dimensional shapes, are objects that have three dimensions: length, width, and height (or depth). Unlike flat, 2D shapes (which only have length and width), 3D shapes have a third dimension, which can be height, depth or thickness.
Each 3D shape has:
- Faces: Flat or curved surfaces.
- Edges: The lines where two faces meet.
- Vertices: The points or corners where edges meet.
Examples of 3D Shapes
Common 3D shapes include cubes, spheres, cones, cylinders, and pyramids. These shapes are found all around us in everyday objects like boxes, balls, and cans.
Cube
- Faces: 6
- Edges: 12
- Vertices: 8
- Properties: All faces are squares, and all angles are right angles.
- Real-Life Example: A dice, a box.
Cuboid (Rectangular Prism)
- Faces: 6
- Edges: 12
- Vertices: 8
- Properties: All faces are rectangles.
- Real-Life Example: A book, a matchbox.
Cylinder
- Faces: 3 (2 circular faces and 1 curved surface)
- Edges: 2 (the two circular edges)
- Vertices: None
- Properties: Two parallel circular faces and a curved surface connecting them.
- Real-Life Example: A soda can, a pencil.
Cone
- Faces: 2 (1 circular face and 1 curved surface)
- Edges: 1 (the circular edge)
- Vertices: 1 (the pointed top)
- Properties: It has a flat circular base and a pointed tip at the top.
- Real-Life Example: An ice cream cone, a traffic cone.
Sphere
- Faces: 1 (a curved surface)
- Edges: None
- Vertices: None
- Properties: Every point on the surface is equidistant from the center.
- Real-Life Example: A basketball, a globe.
Pyramid
- Faces: Varies (1 base and triangular faces)
- Edges: Varies
- Vertices: Varies
- Properties: The base can be a square, triangle, or other polygon, and the triangular faces meet at a point called the apex.
- Real-Life Example: The Great Pyramid of Giza, a pyramid-shaped roof.
Tetrahedron
- Faces: 4 (all triangles)
- Edges: 6
- Vertices: 4
- Properties: All faces are equilateral triangles.
- Real-Life Example: A pyramid with a triangular base.
Properties of 3D Shapes
- Faces are the flat or curved surfaces of the shape.
- Edges are the lines where two faces meet.
- Vertices are the corners where edges meet.
Faces, Vertices and Edges of 3D Shapes
The below table lists the number of faces, edges and vertices in the common 3D shapes.
Net of a 3D Shape
A net of a 3D shape is a two-dimensional pattern that can be folded to form the 3D shape. It shows all the faces of the shape laid out flat. For example, the net of a cube consists of six connected squares that, when folded along the edges, form the cube. Nets help us visualize and understand the structure of 3D shapes and how their surfaces come together. They are often used in geometry to teach the relationship between the faces, edges, and vertices of 3D shapes.
3D Shapes Formulas
All 3D shapes have a surface area and volume. Surface area is the total area of all the faces or surfaces of a 3D shape. It’s like finding out how much wrapping paper you would need to cover the shape completely. For example, the surface area of a cube is the sum of the areas of all six square faces. On the other hand, volume refers to the amount of space inside a 3D shape. It tells us how much a shape can hold or contain. For instance, the volume of a cylinder would indicate how much liquid it can hold. Surface area and volume are important concepts in real-life applications like packaging, construction, and design.
3D Shapes in Real-Life
3D shapes are all around us. Here are some examples of how they are used in real life:
- Cubes and rectangular prisms are used in packaging, like boxes or containers.
- Spheres are used in sports like basketballs, soccer balls, and even in the design of globes.
- Cones are used in traffic signs, party hats, and ice cream cones.
- Cylinders are found in cans, tubes, and columns in buildings.
- Pyramids can be seen in architecture, like ancient monuments or roof designs.
Practice Quiz on 3d-Shapes
FAQs on 3D Shapes
- Euler’s formula for polyhedra is a relationship between the number of faces (F), edges (E), and vertices (V) of a 3D shape. It states that: V−E+F=2. This formula applies to many polyhedra (3D shapes with flat faces, such as cubes or pyramids).
- Yes, prisms and cylinders have two identical, parallel bases (polygonal for prisms and circular for cylinders). These bases define the shape of the 3D object, and the sides connect the two bases.
- Yes, just like 2D shapes, 3D shapes can be irregular. An irregular 3D shape has faces, edges, or angles that are not equal. For example, an irregular polyhedron might have different-sized faces and unequal edges.
Identifying the nets of various 3D shapes can be made easier by understanding the properties of each shape and visualizing how the shape can be unfolded into a flat pattern. Here are some tips and examples to help identify the nets for common 3D shapes:
Cube:
- Net Characteristics:
- A cube has 6 square faces.
- The net consists of 6 connected squares.
Rectangular Prism:
- Net Characteristics:
- A rectangular prism has 6 rectangular faces.
Cylinder:
- Net Characteristics:
- A cylinder has 2 circular bases and a curved surface.
Cone:
- Net Characteristics:
- A cone has a circular base and a curved surface that narrows to an apex.
Pyramid:
- Net Characteristics:
- A pyramid has a polygonal base and triangular faces.