There are 36 results
Broad Topics > 3D Geometry, Shape and Space > Cubes & cuboids
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?
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?
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?
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?
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...?
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.
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.
Paper Folding - Models of the Platonic Solids
Age 11 to 16
A description of how to make the five Platonic solids out of paper.
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?
Christmas Boxes
Age 11 to 14
Challenge Level
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
Icosian Game
Age 11 to 14
Challenge Level
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.
Counting Triangles
Age 11 to 14
Challenge Level
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Take Ten
Age 11 to 14
Challenge Level
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Plutarch's Boxes
Age 11 to 14
Challenge Level
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
How Many Dice?
Age 11 to 14
Challenge Level
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
Boxed In
Age 11 to 14
Challenge Level
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
Tic Tac Toe
Age 11 to 14
Challenge Level
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
Painting Cubes
Age 11 to 14
Challenge Level
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
All in the Mind
Age 11 to 14
Challenge Level
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
NRICH is part of the family of activities in the Millennium Mathematics Project.