There are 71 NRICH Mathematical resources connected to Cubes & cuboids, you may find related items under 3D Geometry, Shape and Space.
Broad Topics > 3D Geometry, Shape and Space > Cubes & cuboids
Always, Sometimes or Never? Shape
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Changing Areas, Changing Volumes
Age 11 to 14 Challenge Level:
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
Triple Cubes
Age 5 to 11 Challenge Level:
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Next Size Up
Age 7 to 11 Challenge Level:
The challenge for you is to make a string of six (or more!) graded cubes.
Partly Painted Cube
Age 14 to 16 Challenge Level:
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Holes
Age 5 to 11 Challenge Level:
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
Cubestick
Age 16 to 18 Challenge Level:
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Sending a Parcel
Age 11 to 14 Challenge Level:
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Cuboids
Age 11 to 14 Challenge Level:
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
The Spider and the Fly
Age 14 to 16 Challenge Level:
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Painted Cube
Age 14 to 16 Challenge Level:
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
The Third Dimension
Age 5 to 11 Challenge Level:
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
A Puzzling Cube
Age 7 to 11 Challenge Level:
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
Marbles in a Box
Age 11 to 16 Challenge Level:
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Nine Colours
Age 11 to 16 Challenge Level:
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?
Cubes Cut Into Four Pieces
Age 5 to 7 Challenge Level:
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Making Cuboids
Age 7 to 11 Challenge Level:
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Cubes
Age 7 to 11 Challenge Level:
How many faces can you see when you arrange these three cubes in different ways?
Nicola's Jigsaw
Age 11 to 14 Challenge Level:
Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?
Which Face?
Age 14 to 16 Short Challenge Level:
Which faces are opposite each other when this net is folded into a cube?
Troublesome Dice
Age 11 to 14 Challenge Level:
When dice land edge-up, we usually roll again. But what if we didn't...?
Three Sets of Cubes, Two Surfaces
Age 7 to 11 Challenge Level:
How many models can you find which obey these rules?
Which Solid?
Age 7 to 16 Challenge Level:
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Castles in the Middle
Age 7 to 14 Challenge Level:
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Solids
Age 11 to 16 Challenge Level:
A task which depends on members of the group working collaboratively to reach a single goal.
The Solid
Age 11 to 16 Challenge Level:
A task which depends on members of the group working collaboratively to reach a single goal.
28 and It's Upward and Onward
Age 7 to 11 Challenge Level:
Can you find ways of joining cubes together so that 28 faces are visible?
Summing Squares
Age 14 to 16 Challenge Level:
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Drilling Many Cubes
Age 7 to 14 Challenge Level:
A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
Start Cube Drilling
Age 5 to 7 Challenge Level:
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
Painted Faces
Age 7 to 11 Challenge Level:
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Cube Drilling
Age 7 to 11 Challenge Level:
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Interpenetrating Solids
Age 16 to 18 Challenge Level:
This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!
Cheese Cutting
Age 16 to 18 Challenge Level:
In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
Paper Folding - Models of the Platonic Solids
Age 11 to 16
A description of how to make the five Platonic solids out of paper.
Making Maths: Link-a-cube
Age 7 to 11 Challenge Level:
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
Cuboid-in-a-box
Age 7 to 11 Challenge Level:
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
All Wrapped Up
Age 7 to 11 Challenge Level:
What is the largest cuboid you can wrap in an A3 sheet of paper?
Classic Cube
Age 16 to 18 Challenge Level:
The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?
Inside Out
Age 14 to 16 Challenge Level:
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
Dice, Routes and Pathways
Age 5 to 14
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
Thinking 3D
Age 7 to 14
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?
All Tied Up
Age 14 to 16 Challenge Level:
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
Classifying Solids Using Angle Deficiency
Age 11 to 16 Challenge Level:
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
Cubist Cuts
Age 11 to 14 Challenge Level:
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
Three Cubed
Age 7 to 11 Challenge Level:
Can you make a 3x3 cube with these shapes made from small cubes?
Dicey
Age 7 to 11 Challenge Level:
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Green Cube, Yellow Cube
Age 7 to 11 Challenge Level:
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?
NRICH is part of the family of activities in the Millennium Mathematics Project.