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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?

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Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Cutting a Cube

Age 11 to 14
Challenge Level

The longest dimension in a cube is the diagonal from top to bottom of opposite vertices. This is shown on this dissection of a cube.

The half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it.

Can you draw a net of these pieces? Are they identical?