Comparing 2D and 3D Shapes

Shapes around us come in two big families: flat shapes and solid shapes. A flat shape, called a 2D shape (two-dimensional shape), has only length and width. It lies completely flat on a piece of paper. A 3D shape (three-dimensional shape) has length, width, and height, so it takes up space and can be picked up and held. Comparing 2D and 3D shapes means looking closely at these features so we can tell the two groups apart and describe each shape using the right words.

Before comparing them, it helps to already be comfortable with 2D shapes and 3D shapes on their own. This lesson brings those two ideas together.

The easiest way to compare a 2D shape and a 3D shape is to ask: can it be drawn flat on paper with just one view, or does it need to be looked at from many sides because it has depth?

• 2D shapes are flat. Examples include a circle, a square, a rectangle, and a triangle. They are described using sides and corners.
• 3D shapes are solid. Examples include a sphere, a cube, a cone, and a cylinder. They are described using faces, edges, and vertices.

Many 3D shapes are built around a familiar 2D shape. Comparing the pair side by side makes the connection easy to see.

When we compare shapes, we should use matching vocabulary for each group. Use the table below as a quick reference.

Feature	2D Shapes	3D Shapes
Dimensions	Length and width	Length, width, and height
Flat or solid	Flat	Solid
Parts counted	Sides and corners	Faces, edges, and vertices
Can it be picked up?	No, it is drawn flat	Yes, it takes up space
Examples	Square, circle, triangle, rectangle	Cube, sphere, cone, cylinder

For a deeper look at counting sides and corners on flat shapes, see sides and corners of 2D shapes. For a closer look at faces, edges, and vertices on solids, see attributes of 3D shapes.

Suppose we have four objects: a piece of paper cut into a hexagon, a soccer ball, a book, and a drawing of a rectangle. Let's compare them one at a time.

• The paper hexagon is flat with 6 sides and 6 corners, so it is a 2D shape.
• The soccer ball is round and can be held in your hands, so it is a 3D shape (a sphere).
• The book has flat faces but also thickness, so it is a 3D shape (like a rectangular prism).
• The drawing of a rectangle only shows length and width on paper, so it is a 2D shape.

Sorting shapes this way, by checking whether an object is flat or whether it has thickness you can feel, is the core skill behind comparing 2D and 3D shapes.

• If a shape can be drawn completely with a pencil on flat paper, it is 2D.
• If a shape needs to be built, molded, or stacked to exist in real life, it is 3D.
• 2D shapes never have faces or edges, only sides and corners.
• 3D shapes are often made of several 2D shapes joined together, like a cube being made of six squares.

Once shapes are sorted, it can also help to check them for symmetry; see symmetry for more on that idea, or review polygons and non-polygons to sharpen how flat shapes are named.

Related lessons

• Math 3