3D shapes and their properties

Can you find ways of joining cubes together so that 28 faces are visible?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Can you make a 3x3 cube with these shapes made from small cubes?

How can you represent the curvature of a cylinder on a flat piece of paper?

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

What is the shape of wrapping paper that you would need to completely wrap this model?

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

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?

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?