The Open Box Problem

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GCSE Maths Investigation

The Open Box Problem

An open box is made form a sheet of card. Identical squares are then cut from each corner, making a cross shape. The card is then folded to make an open-lid box.

The Yellow squares are the shapes, which are removed. The box is made by folding along the dotted lines.

AIM: The main aim of this investigation is to find the relationship between the size of the rectangle cut and the volume of the box. The size of the rectangle cut which makes the volume of the box as large as possible must be determined. Remembering that a square is also a special form of a rectangle.

As well as the general aim there are two other aims:

1. For any sized square sheet of card, investigate the size of the cut out square, which makes an open box of the largest volume.

2. For any sized rectangular sheet of card, investigate the size of the cut out square, which makes an open box of the largest volume.

AIM 1

First I will be looking at aim 1 which uses a square sheet