Read

Identify 2D Shapes in 3D Shapes

This lesson teaches students to recognize the 2D shapes that form the flat faces of common 3D solids, such as cubes, rectangular prisms, cylinders, cones, and pyramids. Students practice counting faces, edges, and vertices, and matching each flat face to the 2D shape it represents.

What does it mean to find a 2D shape inside a 3D shape?

A 3D shape (also called a solid) takes up space, it has length, width, and height. Think of a box, a soup can, or a party hat. If you look closely at the flat, outside surfaces of a 3D shape, you will notice something interesting: those flat surfaces are actually 2D shapes. A 2D shape is flat and only has length and width, like a square, circle, triangle, or rectangle.

Learning to identify 2D shapes in 3D shapes means looking at a solid and naming the flat shapes that cover it. This skill connects directly to what you already know about sorting flat shapes, which you can review in Sort 2D Shapes by attribute, and it sets the stage for building solids out of flat pieces, which is explored in Composing and decomposing 2D Shapes.

Faces, edges, and vertices

Before naming the 2D shapes on a solid, it helps to know three important words used to describe 3D shapes.

Face: a flat surface on a 3D shape. Each face is a 2D shape.
Edge: a line segment where two faces meet.
Vertex (plural: vertices): a point, or corner, where edges meet.

A cube has 6 faces, 12 edges, and 8 vertices. Every one of those 6 faces is a square, so a cube is made entirely of squares.

The highlighted flat surface on each solid shows the 2D shape found on its faces.

Matching common 3D shapes to their 2D faces

Here is a quick reference for some of the most common solids you will see and the 2D shapes that make up their faces.

3D shape	Number of faces	2D shapes found on faces	Edges	Vertices
Cube	6	Square	12	8
Rectangular prism	6	Rectangle (sometimes square)	12	8
Cylinder	2 flat faces + 1 curved surface	Circle	2	0
Cone	1 flat face + 1 curved surface	Circle	1	1
Sphere	0 flat faces	None, fully curved	0	0
Triangular prism	5	Triangle and rectangle	9	6
Square pyramid	5	Square and triangle	8	5

Notice that a sphere, like a ball, has no flat faces at all, so it has no 2D shape hiding inside it. A cylinder and cone both have curved surfaces, but their flat faces are always circles.

Worked examples

Example 1: Look at a cereal box. It is a rectangular prism. Each of its 6 faces is a flat rectangle, so the 2D shape you find on every face is a rectangle.

Example 2: Look at an ice cream cone. It has one flat, round face at the top opening and a curved surface leading down to a point. The 2D shape on its flat face is a circle.

Example 3: A triangular prism, like a tent or a wedge of cheese, has 2 triangular faces on its ends and 3 rectangular faces along its sides. So this solid contains both triangles and rectangles.

Example 4: A square pyramid, like a classic pyramid shape, has 1 square face on the bottom and 4 triangular faces meeting at the top point.

Tips for identifying shapes on solids

Turn the solid in your mind (or in your hands) and look at one face at a time.
Ask whether the face is flat all the way around with straight sides (like a square, rectangle, or triangle) or curved (like a circle).
Count how many of each 2D shape appear before naming all the faces of the solid.
Remember that curved surfaces, like the side of a cylinder or a sphere, are not flat 2D faces.

Once you are comfortable spotting these flat shapes on solids, it also helps to practice describing where shapes sit relative to each other, a skill covered in Describe relative positions of objects, since many real-world solids combine several 2D shapes in different positions.

Related lessons

Math 2