3D shapes and their properties

problem
Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?
problem
Immersion

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

How can you represent the curvature of a cylinder on a flat piece of paper?
problem
Fill me up too

Age

14 to 16

Challenge level

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?
problem
Platonic planet

Age

14 to 16

Challenge level

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
problem
Tet-trouble

Age

14 to 16

Challenge level

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
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
Packing 3D shapes

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?