3D Shapes - Math Steps, Examples & Questions (2024)

Introduction

Common Core State Standards

How to identify 3D shapes

Teaching tips for 3D shapes

Easy mistakes to make

Practice 3D shapes questions

3D shape FAQs

Next lessons

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Here you will learn about 3D shapes, including their names and properties and how to identify and classify 3D shapes.

Students will first learn about 3D shapes in 1 st grade with their work in geometry, identifying and classifying shapes by their properties. They expand their knowledge of 3D shapes as they progress through elementary and middle school.

What are 3D shapes?

3D shapes (three-dimensional shapes) are solid shapes that have 3 dimensions: height, width and depth (all line segments).

Here are some familiar 3D shapes:

Cube	Cone	Pyramid shape	Cylinder

Faces, edges and vertices

Polyhedra are 3D shapes made up of faces, edges and vertices as illustrated below.

Face A flat 2D shape surrounded by edges and vertices.
Edge A straight line where two faces meet and connect two vertices
Vertex A point where two or more edges meet (like a corner)

The shape in the table is a cube. It has 6 faces, 12 edges and 8 vertices.

Properties of 3D Shapes

3D shapes can be categorized in several ways. A 3D shape is either a polyhedra or a non-polyhedra.

3D shapes can then be further categorized as shown in the table below. The properties of 3D shapes can help to classify them and recall their names.

Name of polyhedra	Properties of polyhedra
Rectangular prism A rectangular prism can be described as a cuboid. Step-by-step guide: Rectangular prism	● 6 faces ● 12 edges ● 8 vertices (corners)
Triangular prism Step-by-step guide: Triangular prism	● 5 faces ● 9 edges ● 6 vertices (corners)
Square pyramid Step-by-step guide: Square Pyramid	● 5 faces ● 8 edges ● 5 vertices (corners)
Triangular pyramid (tetrahedron) Step-by-step guide: Triangular Pyramid	● 4 faces ● 6 edges ● 4 vertices (corners)

Name of non-polyhedra	Properties of non-polyhedra
Sphere A sphere can be described simply as a ball. Step-by-step guide: Sphere shape	● All dimensions (length, width and height) are the same. ● The center point is equal from every point on its surface.
Cylinder A cylinder can be described as ‘prism-like’ with a circular base. Step-by-step guide: Cylinder	● 2 circular bases ● 1 curved lateral surface
Cone A cone can be described as ‘pyramid-like’ with a circular base. Step-by-step guide: Cone	● 1 circular base ● 1 curved surface ● 1 apex (vertex)

Step-by-step guide: 3D shape names

Step-by-step guide: Pyramid shape

Volume and surface area of 3D shapes

You can find the volume and surface area of 3D shapes.

The volume of a 3D shape is the amount of space there is inside the shape.

See also: Volume

Surface area is the total area occupied by the surface of a 3D shape.

To find the surface area of a prism, cylinder, or pyramid, it is often helpful to draw the net of the 3D shape, calculate the area of each face, and then add them together.

See also: Surface area

Common Core State Standards

How does this relate to 1 st grade math?

• Grade 1: Geometry (1.G.A.2)
  Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

How to identify 3D shapes

In order to identify a 3D shape, you will:

1. State the characteristics of the given shape.
2. Recall the definitions of the different 3D shapes and state which 3D shape the shape is.

Example 1: identifying 3D shapes

What is the name of this 3D shape?

1. State the characteristics of the given shape.

The given shape has 1 circular base, 1 curved side that meets at the 1 apex on the shape.

2Recall the definitions of the different 3D shapes and state which 3D shape the shape is.

Based on the characteristics of the given shape, the shape is a cone.

Example 2: identifying 3D shapes

Edward is giving Nancy directions to draw a given 3D shape. Edward tells Nancy that the shape has a square base with 4 triangular faces, 8 edges and 5 vertices. What shape is Edward describing to Nancy?

Recall the definitions of the different 3D shapes and state which 3D shape the shape is.

Nancy recalls the shapes that she is familiar with that have a square base,

She now needs to look and see which have 4 triangular faces.

The rectangular prism and cube only have rectangular faces. These are not the shapes Edward was describing.

The triangular prism has 2 triangular faces and 3 square faces. This is not the shape Edward was describing.

The square pyramid has 1 square base and 4 triangular faces. It also has 8 edges and 5 vertices.

Edward was describing a square pyramid to Nancy.

Example 3: real-world example

Look at the image below and determine which 3D shape it is.

State the characteristics of the given shape.

The shape is a basketball, where all dimensions are the same. The center point will be equal from every point on the surface.

Example 4: real-world example

Look at the image below and determine which 3D shape it is.

State the characteristics of the given shape.

This shape has a square base with 4 triangular faces ( 2 showing) and has 5 vertices ( 4 showing).

How to identify 3D shapes in a composite shape

In order to identify 3D shapes in a composite shape, you will:

1. Count the number of shapes that make up the composite shape.
2. Identify and state the number of each type of shape within the composite shape.

Example 5: identifying 3D shapes in a composite shape

Look at the composite shape and identify all 3D shapes.

Count the number of shapes that make up the composite shape.

There are two shapes in this composite shape.

Example 6: identifying 3D shapes in a composite shape

Look at the composite shape and identify all 3D shapes.

Count the number of shapes that make up the composite shape.

There are \bf{7} shapes in this composite shape.

Teaching tips for 3D shapes

• Find a 3D shapes song for kids to introduce and reinforce important vocabulary and concepts. Songs often contain repetitive lyrics, which reinforce the material being learned, so when students listen to or sing a song repeatedly, the information becomes ingrained in their working memory and helps recall.

• Teach terms like faces, edges, vertices, and base and incorporate these terms during discussions and activities.

• Printable worksheets that show a variety of 3D shapes or real-life examples can be useful for students to practice with. Students need to practice not being able to “see” all sides of the geometric shape, but still identify all the characteristics.

Easy mistakes to make

• Using the wrong formula
  There are several formulas for surface area and volume. Make sure you select the right one by correctly identifying the 3D shape in the question and what it is asking you to calculate.

• Using a mixture of units in a calculation
  When you are calculating volume or surface area, you must ensure that the units of length you are using are the same. This may mean that you need to convert a unit before you carry out a calculation. For example, if one length is given in meters and another is given in centimeters, you must convert one of them so that they are either both in meters or both in centimeters.

• Missing or incorrect units
  You should always include units in your final answer.
  Surface area is measured in square units (for example, mm^{2}, cm^{2}, m^{2}, etc.).
  Volume is measured in units cubed (for example, mm^{3}, cm^{3}, m^{3}, etc.).

  For volume, you may also be asked to give your answer in liters or millimeters for example. Note that,
  1 \, ml = 1 \, cm^{3}
  1 \, liter = 1000 \, ml = 1000 \, cm^{3}

• Not counting “hidden” faces, edges and vertices
  When counting the faces, edges or vertices on an image of a 3D shape, you should consider if there are any that are ‘hidden’. Some drawings use dashed lines to represent edges that cannot be seen but sometimes they do not. In this case, try and visualize if there are any ‘hidden’ faces, edges, or vertices behind or underneath the 3D representation.

What is the difference between 2D and 3D shapes?

How do you identify a 3D shape?

To identify a 3D shape, you need to consider its properties. Look for features like faces (the flat surfaces), edges (the lines where two faces meet), and vertices (the points where edges meet). The number and arrangement of faces, edges, and vertices can help you determine the specific 3D shape.

The next lessons are

• Surface area
• Volume
• Area of a quadrilateral
• Prism shape
• Hemisphere shape

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