3D shapes and their properties

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

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

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 ?

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

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

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

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

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?

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

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.