Cubes and cuboids

There are 81 NRICH Mathematical resources connected to Cubes and cuboids

problem

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.

problem

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?

problem

Cubic conundrum

Age

7 to 16

Challenge level

Which of the following cubes can be made from these nets?

problem

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?

problem

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?

problem

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.

problem

Cubic vision

Age

14 to 16

Challenge level

How many cubes can you see?

problem

Wrapping gifts

Age

16 to 18

Challenge level

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

problem

More christmas boxes

Age

7 to 11

Challenge level

What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?

problem

All wrapped up

Age

7 to 11

Challenge level

What is the largest cuboid you can wrap in an A3 sheet of paper?

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For younger learners

Cubes and cuboids

Icosian game

Classic cube

Cubic conundrum

Summing squares

All in the mind

Christmas boxes

Cubic vision

Wrapping gifts

More christmas boxes

All wrapped up