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?

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.