2D representations of 3D shapes

There are 45 NRICH Mathematical resources connected to 2D representations of 3D shapes
Guess What?
problem

Guess what?

Age
7 to 11
Challenge level
filled star empty star empty star
Can you find out which 3D shape your partner has chosen before they work out your shape?
Nine Colours
problem

Nine colours

Age
11 to 16
Challenge level
filled star filled star filled star
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?
Arranging cubes
problem

Arranging cubes

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

A task which depends on members of the group working collaboratively to reach a single goal.

The Third Dimension
problem

The third dimension

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Which solids can we make?
problem

Which solids can we make?

Age
11 to 14
Challenge level
filled star filled star filled star

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Building Blocks
problem

Building blocks

Age
7 to 11
Challenge level
filled star empty star empty star
Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
The Spider and the Fly
problem

The spider and the fly

Age
14 to 16
Challenge level
filled star filled star empty star
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?
Hamiltonian Cube
problem

Hamiltonian cube

Age
11 to 16
Challenge level
filled star filled star empty star
Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
Picture a Pyramid ...
problem

Picture a pyramid

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

A City of Towers
problem

A city of towers

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?