The Open Box Investigation

The Open Box Investigation

The aim of this investigation is to find the largest volume within for

an open box with any size square cut out

I will be increasing the square cut out by 1cm until I reach a point

where the volume decreases. At this point I will decrease the square

cut out by 0.1cm until I reach the maximum volume. This will be done

on several different grids until I see a pattern which I will then use

to create a formula.

I will record my results in a table for the different grids and record

the peaks to try and establish a pattern.

My initial grid size will be 12cm x 12cm and I will increase this as I

continue my investigation. The volume will be calculated by

multiplying the length by the width by the height. When I appear to

reach a maximum volume I will try cut sizes 0.1cm smaller and larger

than the cut size that appears to give the maximum volume. If the

volume increases then I will make the cut size smaller or larger by

0.1cm again. I will repeat this for grid sizes of 18cm x 18cm and 24cm

x 24cm.

I have found the following results:

Grid Size: 12cm x 12cm

Cut Size

Calculation

Volume

1cm

10 x 10 x 1

100cm3

2cm

8 x 8 x 2

128cm3

3cm

6 x 6 x 3

108cm3

1.9cm

8.2 x 8.2 x 1.9

127.8cm3

2.1cm

7.8 x 7.8 x 2.1

127.8cm3

Grid Size: 18cm x 18cm

Cut Size

Calculation

Volume

1cm

16 x 16 x 1

256cm3

2cm

14 x 14 x 2

392cm3

3cm

12 x 12 x 3

432cm3

4cm

10 x 10 x 4

400cm3

2.9cm

12.