Cubes and cuboids

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Are these statements always true, sometimes true or never true?

Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?

Can you create more models that follow these rules?

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

How many cubes can you see?

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?

What is the largest cuboid you can wrap in an A3 sheet of paper?