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Six Discs

Age 14 to 16 Challenge Level:

Six circular discs, all of radius 1 unit, are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box.

  • Without using any calculations, compare the areas of the bases of boxes A and B and say which is the larger.
  • Use estimation to list the packings in order of increasing base area. Which are the hardest to put in order?
  • Now calculate the area of the base of each box and compare the correct order with your estimate.