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?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
What is the largest cuboid you can wrap in an A3 sheet of paper?
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
If you had 36 cubes, what different cuboids could you make?
A box has faces with areas 3, 12 and 25 square centimetres. What is
the volume of the box?
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?
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. . . .