2. Car Registration Discs An Investigation

3. 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. 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 30cm 50cm

4. 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. 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 5/1/03 Disc 30cm 50cm

5. 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?

6. 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.

7. It is possible to get 19.5% waste by stacking as indicated in the diagram below. Trigonometry is needed to look at this arrangement. 35cm 19.1cm