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MaxBox

MaxBox. 24cm. 20cm. Which gives a box that looks like this. When we cut out a 5cm square we get this box. What happens if we cut out a smaller square?. What happens if we cut out a larger square?. Which box has the largest volume?. MaxBox. 24cm. 5cm. 20cm. MaxBox. 24cm. Height = ?.

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MaxBox

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  1. MaxBox 24cm 20cm

  2. Which gives a box that looks like this

  3. When we cut out a 5cm square we get this box.

  4. What happens if we cut out a smaller square?

  5. What happens if we cut out a larger square? Which box has the largest volume?

  6. MaxBox 24cm 5cm 20cm

  7. MaxBox 24cm Height = ? 20cm

  8. MaxBox 24cm Height = 5 20cm

  9. MaxBox 24cm Height = 5 Length = ? 20cm

  10. MaxBox 24cm Height = 5 5 5 Length = 14 20cm

  11. MaxBox 24cm Height = 5 Length = 14 Width = ? 20cm

  12. MaxBox 24cm 5 Height = 5 Length = 14 Width = 10 20cm 5

  13. Volume of this box Volume = length x width x height Volume = 14 x 10 x 5 = 700 cm3

  14. Working as a table you have 4 tasks to tackle:

  15. Find the largest box you can make if you start with a piece of card 30 cm by 20 cm

  16. Find the largest box you can make if you start with a piece of card 25 cm by 25 cm

  17. Find the largest box you can make if you start with a piece of card 60 cm by 12 cm

  18. If the largest volume for a piece of card which is 20cm by 20cm is 592.6 cm3 What is the largest volume for a piece of card which is: 40 cm by 40 cm? 10 cm by 10 cm? 40 cm by 20 cm? Extension Task

  19. Possible Approaches? • Cut out a different sized square • 4cm or 6cm • By making the models • Without making the models - explain • Use the graph to estimate maximum • Use decimals • Use a spreadsheet

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