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  • Early Years Foundation Stage

Take Ten

Age 11 to 14
Challenge Level Yellow starYellow starYellow star
  • Problem
  • Student Solutions

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3 cube? In how many different ways can this be done?

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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?

Cubic Conundrum

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

Cuboids

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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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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