... included in this diagram the labels c, x and y, these show the cut out size and the original length and width of the card, I will now need to show the values of the width, length and height in terms of c, x and y. Therefore I can replace these sub formulae into the first formula. However for the values of a square, y=x therefore: c V 1 324 2 512 3 588 4 576 5 500 6 384 7 252 8 128 9 36 As I have already said, the value of x is 20cm and I will use a range of values for c, then I will plot a graph with c on the x-axis and the volume (V) on the y-axis. At the peak, the value on the x-axis will be the cut size that gives the maximum volume. x=12 c V 1 100 2 128 3 108 4 64 5 20 For this value of x, the maximum cut size I could cut out would be 5cm, yet these results were clear and showed a very good ...

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