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'Classic Cube' printed from http://nrich.maths.org/
I have a large square piece of card 100cm along each side and have decided to make a large cube from it.
I could cut the net of the cube so that its sides are parallel to the sides of the card and, ignoring any tabs needed to join the edges together, it could look like this:
What is the volume of this cube?
However, I am wasting a lot of the card by cutting the net in this way and I think I can create a cube with a larger volume if I place a net diagonally on the card, like this:
What are the dimensions of the cube with greatest volume I can cut from the card by using different nets and aligning them at an angle to the sides of the card?