There are 45 NRICH Mathematical resources connected to 3D shapes and their properties, you may find related items under 3D geometry, shape and space.
Broad Topics > 3D geometry, shape and space > 3D shapes and their properties
Can you find out which 3D shape your partner has chosen before they work out your shape?
Are these statements always true, sometimes true or never true?
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?
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
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 ?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Here are shadows of some 3D shapes. What shapes could have made them?
Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
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.
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
How many faces can you see when you arrange these three cubes in different ways?
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.
In this article for primary teachers, Ems explores ways to develop mathematical flexibility through geometry.
What is the shape of wrapping paper that you would need to completely wrap this model?
How can you represent the curvature of a cylinder on a flat piece of paper?
Can you find ways of joining cubes together so that 28 faces are visible?
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
A description of how to make the five Platonic solids out of paper.
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?
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?
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.
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.
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.
Can you make a 3x3 cube with these shapes made from small cubes?
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.
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?
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?
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?
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.
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?
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?
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?
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?
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Make a cube out of straws and have a go at this practical challenge.