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Three Cubes

Can you work out the dimensions of the three cubes?

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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.

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Cubic Conundrum

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

Peeling the Apple or the Cone That Lost Its Head

Age 14 to 16 Challenge Level:

This is a nice activity to take slowly and build up understanding in each part.

It also makes a nice lead in towards maths at the next level, especially if the spreadsheet is used to improve accuracy as each fustum height becomes smaller without limit.