Investigation 1-Square shaped pieces of card

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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.              Height is also the same as to the size of the cut-out corners of an open box.

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I am going to begin by investigating a square with a side length of 12 cm. Using this side length, the maximum whole number I can cut off each corner is 5cm, as otherwise I would not have any box left.

 

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 ...

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