3D Shapes Worksheets

3D shapes, or solids, have length, width and height, so they take up space: a box, a ball and a can are all 3D shapes. The four PDFs on this page ask children to name solids from a word bank and to count the faces, edges and vertices of prisms and pyramids, and every sheet has an answer key. They follow standards K.G.A.3, 1.G.A.1 and 2.G.A.1 of the Common Core standards for kindergarten geometry, and the notes below show how the counts work.

Faces, edges and vertices

A face is a flat surface, an edge is where two faces meet, and a vertex is a corner where edges meet. A cube has 6 faces, 12 edges and 8 vertices. The drawings on these worksheets show hidden edges as dashed lines, so children can count the ones at the back too.

3d shapes worksheets: what is in the set

There are 4 3d shapes worksheets on this page, and every one has an answer key except for any cut-out games. Two sets ask children to name the solid, and two sets ask them to count the faces, edges and vertices.

3D shapes: faces, edges and vertices of the solids

A face is a flat surface of a solid, an edge is a line where two faces meet, and a vertex is a corner where edges meet. Solids with only flat faces are called polyhedra, and Wikipedia’s article on polyhedra lists them. Solids with curved surfaces, such as a cylinder, a cone and a sphere, have different counts. This table gives the numbers for the eight solids on the worksheets:

The cylinder and the cone have curved edges, where a flat face meets a curved surface, and the sphere has no edges at all. This is the reason why the counting worksheets use only prisms and pyramids, and why the naming worksheets use all eight solids.

Faces edges and vertices worksheets: counting rules for prisms and pyramids

The faces edges and vertices worksheets use prisms and pyramids, and for these there are simple rules. If the base has n sides, a prism has n + 2 faces, 3n edges and 2n vertices, and a pyramid has n + 1 faces, 2n edges and n + 1 vertices. The table shows both for bases from 3 to 8 sides:

A cube is a prism with a square base, so n = 4, and the rule gives 6 faces, 12 edges and 8 vertices. Children do not need the rules in grade 1 or 2, but they help to check a count: a pyramid always has twice as many edges as its base has sides.

Euler’s formula for solids

For every solid with flat faces and no holes, the number of vertices minus the number of edges plus the number of faces is 2. The formula was found by Leonhard Euler in the 1750s. It is a good way to check a count, and to find a missing number. This table tests it for seven solids:

If a child counts 8 vertices and 12 edges for a cube, then the formula gives 8 − 12 + F = 2, so F = 6. This is also a way to see if a count is wrong. The rule does not work for a cylinder, a cone or a sphere, which have curved surfaces.

Solid shapes worksheets: nets and flat faces

The solid shapes worksheets show solids in drawings, but children also meet them as nets, which are the flat patterns that fold up to make a solid. A net shows the flat faces of the solid, and counting them is another way to count faces. This table shows six solids, with the shapes in each net:

There are exactly 11 different nets for a cube, which makes a good puzzle for a class: cut out six squares and try all the ways to join them. The same idea comes back in grade 6 (6.G.A.4), when children use nets to find surface area. The volume calculator works out the volume of the same solids.

3D shapes grade 2: solids in the real world

For 3D shapes grade 2, it helps to link every solid to an object that children know. A die is a cube, a can is a cylinder, and a party hat is a cone. This table gives seven examples with the standard that is linked to each:

Children can build a 3D shapes collection from objects in a classroom or at home, and sort them by the shape of their faces. A good game is to find an object for every solid in the table in a week.

Naming 3D shapes: the 2D shapes on the faces

When naming 3D shapes, children sometimes mix them up with the flat shapes, such as saying that a ball is a circle. A good way to teach the difference is to look at the faces of a solid, because each flat face is a 2D shape. This table shows the 2D shapes that make up each solid:

The 2D shapes page has the flat shapes. A circle is a flat shape on a page, and a sphere is a solid that can be held in the hand.

Common mistakes with 3D shapes

The mistakes are about the difference between faces, edges and vertices, and between 2D and 3D. This table shows five mistakes, what went wrong and the fix:

3d shapes word problems

Story problems use the solids that children know. Ask them to draw the solid first, and to say whether they are counting faces, edges or vertices:

Games and activities for 3d shapes

Children learn 3d shapes best when they play with it. These games use things that are found at home or in a classroom:

• Solid sort: sort household objects into cubes, cylinders, cones, spheres and prisms
• Mystery solid: one child feels a solid in a bag and describes its faces
• Clay and straws: build a cube and a pyramid with straws and clay balls, and count the vertices
• Net puzzle: cut out six squares and find all the nets that fold into a cube
• Shape detectives: find an object that is a cube, a cylinder or a sphere in the kitchen
• 3D shape bingo: a bingo card with solid names and calling cards with pictures

Extra support and extra challenge with 3d shapes

For children who need more support: start with objects the child can hold, such as a die, a can and a ball, and ask “how many flat faces?”. Put a sticker on each face as it is counted. Practice the naming sets before the counting sets, and use a solid in the hand for every counting problem.

For children who need more challenge: ask for a solid that has 6 faces and 8 vertices, to explain why a pyramid always has twice as many edges as its base has sides, and to use Euler’s formula to find a missing number. The “Faces, Edges and Vertices (Set B)” worksheet is a good challenge.

How to tell that a child is ready to move on from 3d shapes

1. The child names the cube, prism, pyramid, cylinder, cone and sphere.
2. The child counts the faces, edges and vertices of a cube.
3. The child says which solids have curved surfaces.
4. The child finds the 2D shapes on the faces of a solid.

When all four are true, move on to the symmetry page or the angles page.

A 20-minute lesson on 3d shapes

A short lesson is the best way to introduce 3d shapes. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where 3d shapes fits across the grades

No skill stands alone. This table shows what children learn before and after 3d shapes, with the standard that goes with each step:

This page leads from flat shapes to measuring solids. The whole sequence is on the geometry worksheets page.

Helping at home with 3d shapes

Parents do not need to be experts to help with 3d shapes. These suggestions work well, and each takes only a few minutes:

• Look for cubes, cylinders and spheres in the kitchen.
• Build a house out of boxes and name each solid.
• Ask “how many faces does this box have?” and let the child count them.
• Use clay to build a cube and a pyramid.
• Check the counts with the answer key.

How to check progress in 3d shapes

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for 3d shapes

Most children need about a week of short sessions for 3d shapes. This plan follows the order of the worksheets on this page:

When the plan is complete, move on to the symmetry page. The whole sequence is on the geometry worksheets page.