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Three Cubes

Can you work out the dimensions of the three cubes?

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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.

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Cubic Conundrum

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

Tin Tight

Age 14 to 16 Challenge Level:

This is a useful application of Trial and Improvement.

It is not necessary to use a lot of algebra for representation where students are not sufficiently confident with that.

A systematic record of the calculation process being repeated is however very important.

A spreadsheet that allows volume to vary is powerful but only after students have established an understanding of the calculation process being carried out by the computer on their behalf.