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Cuboid Challenge

Age 11 to 16
Challenge Level Yellow starYellow star
Secondary curriculum
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Cuboid Challenge printable sheet


Take a square sheet of paper 20cm by 20cm, cut identical squares from each corner, and fold up the flaps to make a box (without a lid).

  

What is the volume of your box?
What different volumes can you make by varying the size of the squares you cut out?

What is the maximum possible volume of this type of box that can be made from a 20cm by 20cm square of paper?

Now try starting with different sized square sheets of paper.

Can you find a relationship between the size of paper and the size of the square cut-out that produces the maximum volume?



Click here for a poster of this problem.

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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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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