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# Maximum Box Investigation

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Introduction

Maximum Box Investigation Question: You have a square sheet of card 24cm by 24cm. You can make a box (without a lid) by cutting squares from the corners and folding up the sides. What size corners should you cut so that the volume of the box is as large as possible? The first step to evaluating the maximum possible volume that the box could contain is to find the area of the paper. This is simply 24cm x 24cm = 576cm�. Now that we have the area, it is easy to evaluate the maximum volume in a variety of different shapes. ...read more.

Middle

To find the volume of this particular cube, we need to cube 10.73 which gives us 1235.37. The volume of this cube is 715.575 cm�. However, the question instructs to fold and cut, which will need a list of results in a table: Table for card 24cm x 24cm Length of the side of the corner square (cm) Dimensions of the open box (cm) Volume of the box (cm�) 1 22 x 22 x 1 484 2 20 x 20 x 2 800 3 18 x 18 x 3 972 4 16 x 16 x 4 1024 5 14 x 14 x 5 980 6 12 x 12 x 6 ...read more.

Conclusion

Dimensions of the open box (cm) Volume of the box (cm�) 1 13 x 13 x 1 169 2 11 x 11 x 2 242 3 9 x 9 x 3 243 4 7 x 7 x 4 196 5 5 x 5 x 5 125 Investigate the situation when the card is not square. Take rectangular cards where the length is twice the width (20 x 10, 12 x 6, 18 x 9 etc.) Again, for the maximum volume is there a connection between the size of the corners cut out and the size of ...read more.

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