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Covering Cups

What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.

Cutting a Cube

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?