Cubes and cuboids

There are 81 NRICH Mathematical resources connected to Cubes and cuboids
Cuboids
problem
Favourite

Cuboids

Age
11 to 14
Challenge level
filled star filled star filled star
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?
Inky Cube
problem
Favourite

Inky cube

Age
7 to 14
Challenge level
filled star filled star filled star

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Making Cuboids
problem
Favourite

Making cuboids

Age
7 to 11
Challenge level
filled star filled star empty star
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?
Marbles in a box
problem
Favourite

Marbles in a box

Age
11 to 16
Challenge level
filled star filled star empty star
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Holes
problem
Favourite

Holes

Age
5 to 11
Challenge level
filled star empty star empty star

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?

Cubes Cut into Four Pieces
problem
Favourite

Cubes cut into four pieces

Age
5 to 7
Challenge level
filled star filled star filled star
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?
Sending a Parcel
problem
Favourite

Sending a parcel

Age
11 to 14
Challenge level
filled star filled star empty star
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Cubestick
problem
Favourite

Cubestick

Age
16 to 18
Challenge level
filled star filled star empty star
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Three cubes
problem
Favourite

Three cubes

Age
14 to 16
Challenge level
filled star filled star empty star
Can you work out the dimensions of the three cubes?
A Puzzling Cube
problem
Favourite

A puzzling cube

Age
7 to 11
Challenge level
filled star empty star empty star

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?