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Three Cubes

Can you work out the dimensions of the three cubes?


At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

Cubic Conundrum

Which of the following cubes can be made from these nets?

Tin Tight

Age 14 to 16
Challenge Level
What are the most efficient proportions for a tin of paint?

"Efficient" could mean different things from different points of view - maybe start by trying to minimise the amount of material needed to make a tin with that volume.

What is the best diameter and height for a tin that contains $1$ litre of paint?

What about a $5$ litre tin?