3D shapes and their properties

Can you find out which 3D shape your partner has chosen before they work out your shape?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

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

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?

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 ?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

How many faces can you see when you arrange these three cubes in different ways?