Investigating the Volume of an Open Box
The aim of this coursework is to investigate the volume of an open box
constructed by one piece of rectangular card that has all four corners
having had squares cut out of them. Firstly I will be studying the
volume whilst changing the side of one length of the cut out square
and the size of the original rectangle card. After I have investigated
this relationship I will try to find out the formula for finding the
cut size to get the largest volume for any specified original card
size.
Square card size
I am going to begin by investigating a square card because this will
give me a basic formula which I can elaborate on. I will start with a
round number of 20cm for the length. This means that the maximum cut
out square length I can cut out will be 9cm else I will have no box
left.
The formula for the volume of any box is as follows:
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Below, there is a diagram to explain where all these figures come
from.
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I have also 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
ofc, x and y.
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Therefore I can replace these sub formulae into the first formula.
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However for the values of a square, y=x therefore:
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c
V
1
324
2
512
3
588
4
576
5
500
6
384
7
252
8
128
9
36
Unfortunately the value I have chosen for x (20) does not show a very
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