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There are **48** NRICH Mathematical resources connected to **3D shapes and their properties**, you may find related items under 3D geometry, shape and space.

Problem
Primary curriculum
Secondary curriculum
### Guess What?

Can you find out which 3D shape your partner has chosen before they work out your shape?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fill Me up Too

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Solids Can We Make?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triple Cubes

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Immersion

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Funnel

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cola Can

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shadow Play

Here are shadows of some 3D shapes. What shapes could have made them?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Building Blocks

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cut Nets

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sponge Sections

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles to Tetrahedra

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Skeleton Shapes

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Marbles in a Box

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nine Colours

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tet-trouble

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Building with Solid Shapes

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cubes

How many faces can you see when you arrange these three cubes in different ways?

Age 7 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Going Deeper: Achieving Greater Depth with Geometry

This article for Primary teachers outlines how providing opportunities to engage with increasingly complex problems, and to communicate thinking, can help learners 'go deeper' with geometry.

Age 5 to 11

Article
Primary curriculum
Secondary curriculum
### Let's Get Flexible with Geometry

In this article for primary teachers, Ems explores ways to develop mathematical flexibility through geometry.

Age 5 to 11

Problem
Primary curriculum
Secondary curriculum
### Auditorium Steps

What is the shape of wrapping paper that you would need to completely wrap this model?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Moving Squares

How can you represent the curvature of a cylinder on a flat piece of paper?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 28 - Upward and Onward

Can you find ways of joining cubes together so that 28 faces are visible?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Packing 3D Shapes

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangular Faces

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Age 7 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Paper Folding - Models of the Platonic Solids

A description of how to make the five Platonic solids out of paper.

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### Thinking 3D

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### A Chain of Eight Polyhedra

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dodecawhat

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

Age 14 to 16

Article
Primary curriculum
Secondary curriculum
### Volume of a Pyramid and a Cone

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Age 11 to 14

Problem
Primary curriculum
Secondary curriculum
### Three Cubed

Can you make a 3x3 cube with these shapes made from small cubes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Icosian Game

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Child's Play

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dodecamagic

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Redblue

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Face Painting

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tetrahedron Faces

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tetra Inequalities

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Platonic Planet

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Points on a Cube

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Proximity

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Double Your Popcorn, Double Your Pleasure

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Construct-o-straws

Make a cube out of straws and have a go at this practical challenge.

Age 7 to 11

Challenge Level