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Three Cubes

Can you work out the dimensions of the three cubes?

Boxed In

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

Cuboid Challenge

Age 11 to 16
Challenge Level

It might be a good idea to work systematically:
Start by cutting out a 1cm square from each corner - what would the volume be?
Then a 2cm square, then a 3cm square, and so on...

The side length of the square doesn't necessarily have to be a whole number...

Perhaps it would help to use a spreadsheet to perform and record your calculations.