# Investigation 1-Square shaped pieces of card

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Introduction

Investigation 1-Square shaped pieces of card

Aim- To find the length of the cut-out corners that gives the maximum volume for the open box formed by any sized piece of square card. The length of the cut out will be given to three significant figures of accuracy.

Method- I will investigate what length of cut-out corners will give the largest volume of square pieces of card with dimensions of 12x12, 18x18, 24x24 and 30x30.

Note- When “length”, “breadth” and “height” are mentioned, they refer to the dimensions of an open box. When “volume” is mentioned, it refers to the volume of an open box.

Middle

I am going to begin by looking into whole numbers being cut out of the box corners.

The formula that needs to be used to get the volume of a box is:

## Volume = Length * Width * Height

If I am to use a square of side length 12cm, then I can calculate the side lengths minus the cut out squares using the following equation.

Volume = Length – (2 * Cut Out) * Width – (2 * Cut Out) * Height

Using a square, both the length & the width are equal. I am using a length/width of 12cm. I am going to call the cut out “x.” Therefore the equation can be changed to:

Volume = 12 – (2x)

Conclusion

Turn to next 2 pages. >

From the tables and graphs I can see that the square cut-out of 5cm gave the largest volume of the open box. I can see that my prediction was correct so therefore I have now worked out a formula for square shaped pieces of card.

Formula to give the maximum open box volume for square shaped pieces of card:

X= Square sized piece of card

X/6= Side of cut-out corner

Volume= Length x Breadth x Height

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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