3D shapes and their properties

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

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?

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

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?

Can you work out the dimensions of the three cubes?

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

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?

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 ?