3D Shapes: Age 11-16

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.

problem
Favourite

Triangles to Tetrahedra

Age

11 to 14

Challenge level

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

Marbles in a Box

Age

11 to 16

Challenge level

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

Nine Colours

Age

11 to 16

Challenge level

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?
problem
Favourite

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?