Car Registration Discs

1
Car Registration Discs

• An Investigation

2

• Car Registration Discs
• Circular discs of radius 3.5cm are to be cut
  from a rectangular sheet of cardboard measuring
  50cm by 30cm. Once the discs are cut out, the
  remaining parts of the sheet are waste.
• The idea is shown in the diagram above.

3

• 1. How many discs can be cut from one sheet
  of cardboard?
• 2. If Waste
• calculate the percentage waste for this
• size of cardboard sheet .

4

• Calculate the percentage waste for sheets
  measuring
• a) 40cm by 35cm b) 70cm by
  63cm
• Investigate different sizes of cardboard and find
  
• the size's which will make the percentage
• waste a minimum.
• Is it possible to reduce the waste further by
  using a different arrangement in cutting out
  discs?

5

• Solution
• (i) 28 discs
• (ii) waste 28.2
• (iii) a) 31.3 b) 21.4
• Pupils should try a number of possible sheets and
  reach the conclusion that the minimum waste
  occurs when the length and the breadth are
  multiples of 7.

6

• It is possible to get 19.5 waste by stacking as
  indicated in the diagram below.
• Trigonometry is needed to look at this
  arrangement.