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This is a useful application of Trial and Improvement.
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.
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F'arc'tion
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.
