3D shapes and their properties

problem
Packing 3D shapes

Age

14 to 16

Challenge level

What 3D shapes occur in nature. How efficiently can you pack these shapes together?
problem
Triangular faces

Age

7 to 11

Challenge level

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
problem
Funnel

Age

14 to 16

Challenge level

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
problem
Cola can

Age

11 to 14

Challenge level

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
problem
Hamiltonian cube

Age

11 to 16

Challenge level

Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
problem
Shadow play

Age

5 to 7

Challenge level

Here are shadows of some 3D shapes. What shapes could have made them?
problem
Building blocks

Age

7 to 11

Challenge level

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
problem
A chain of eight polyhedra

Age

7 to 11

Challenge level

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?
problem
Cut nets

Age

7 to 11

Challenge level

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
problem
Sponge sections

Age

7 to 11

Challenge level

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.