Car Registration Discs

An Investigation

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.

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

30cm

50cm

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 .

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

5/1/03Disc

30cm

50cm

%100totalarea

waste

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?

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.

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