Cubes and cuboids

There are 81 NRICH Mathematical resources connected to Cubes and cuboids

problem

Favourite

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?

problem

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Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?

problem

Favourite

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?

problem

Favourite

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?

problem

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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?

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Next size up

Age

7 to 11

Challenge level

The challenge for you is to make a string of six (or more!) graded cubes.

problem

Favourite

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.

problem

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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?

problem

Favourite

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.

problem

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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?

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For younger learners

Cubes and cuboids

Changing areas, changing volumes

Three cubes

A puzzling cube

Partly painted cube

The third dimension

Next size up

Castles in the middle

Painted cube

Which solid?

Nine colours