Cubes and cuboids

There are 81 NRICH Mathematical resources connected to Cubes and cuboids

problem

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

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?

problem

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?

problem

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.

problem

Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?

problem

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

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

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?

problem

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

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.

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For younger learners

Cubes and cuboids

Changing areas, changing volumes

Cubes cut into four pieces

Sending a parcel

Cubestick

Three cubes

A puzzling cube

Partly painted cube

The third dimension

Next size up

Castles in the middle