We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
What is the largest cuboid you can wrap in an A3 sheet of paper?
If you had 36 cubes, what different cuboids could you make?
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?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Are these statements always true, sometimes true or never true?
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .