Identify Shapes Traced from Solids

Some solids have curved surfaces instead of flat faces. A curved surface will not sit still against a pencil the way a flat face does, so it cannot be traced into a clean shape. This is why a ball, which is a sphere, cannot be traced at all: it has no flat face anywhere on it, only one curved surface. A solid must have at least one flat face before it can trace a 2D shape.

Once you know a solid's faces, you can predict exactly which 2D shape it will trace:

• A cube has 6 square faces, so tracing any face makes a square.
• A rectangular prism has flat rectangular faces (and sometimes square ends), so tracing a face usually makes a rectangle.
• A cylinder has two flat circular faces, one on the top and one on the bottom, so tracing either one makes a circle.
• A cone has one flat circular base, so tracing that base makes a circle. The pointed, curved part cannot be traced.
• A square pyramid has one square base and triangle-shaped side faces, so it can trace either a square or a triangle depending on which face is placed down.
• A sphere has no flat face at all, so it cannot trace any 2D shape.

Comparing these solids side by side is good practice for naming and selecting 3D shapes, since knowing a solid's name usually tells you right away how many faces it has and what shape they are.

Use these steps whenever you are shown a traced outline and asked which solid it came from, or shown a solid and asked what it would trace:

1. Look at the solid and find its flat faces. Skip any curved surfaces since they leave no clean outline.
2. Look closely at just one flat face. Is it a square, a rectangle, a circle, or a triangle?
3. Picture pressing that one face flat against paper and tracing around its edge.
4. Match that outline to the correct 2D shape name.

For example, imagine a can of soup lying on the table. Its flat, round ends are circles, so standing the can upright and tracing the bottom makes a circle. If you instead tried to trace the curved side of the can, the pencil could not follow one flat line, so no clean 2D shape would appear.

A student is given a small wooden box shaped like a cube and asked, "What shape will you get if you trace one face?" First, they check the solid for flat faces and find six of them, all the same size. Next, they look at one face and see it has four equal sides and four corners. That description matches a square, so tracing any face of the cube produces a square.

Another student traces the base of a party hat shaped like a cone. The base is flat and round, so the trace is a circle, even though the rest of the hat comes to a point.

Learning to connect solids to the shapes they trace builds a bridge between 3D and 2D geometry. It also strengthens the vocabulary of faces, edges, and vertices that students will use throughout geometry. Once tracing feels familiar, it is a short step to noticing that the everyday objects around a room, like a cereal box or a can, are really just solid shapes in disguise; that idea is explored further in shapes of everyday objects. It is also useful to review how solid and flat shapes differ overall in comparing 2D and 3D shapes.

• What 2D shape do you get by tracing the face of a rectangular prism? A rectangle.
• Can you trace a shape from a sphere? No, because it has no flat face.
• What shape does tracing the base of a cone make? A circle.
• What two different shapes can a square pyramid trace? A square and a triangle.

Related lessons

• Kindergarten