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# The Open Box Problem

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• Essay length: 2159 words
• Submitted: 05/09/2003
GCSE Open Box Problem

The first 200 words of this essay...

The Open Box Problem

An open box is to be made from a sheet of card as shown below. The corner squares are to be cut-off.

The card is then folded along the dotted lines to make the box.

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part 1 - Square shaped pieces of card

Aim - To find the length of the cutout corners that gives the maximum volume for the open box formed for any sized piece of square card. The length of the square cut will be to 3 significant figures of accuracy.

Method - I will investigate what length of cut-out corners will give the largest volume for square pieces of card with dimensions 12 x 12, 18 x 18,and 30 x 30.

NOTE - when 'small side' is mentioned, it refers to the size of the cut-out corners.

When 'Length', 'Width' and 'Height' are mentioned, they refer to the dimensions of the open box.

When 'Volume' is mentioned, it refers to the volume of the open box.

Rows in Italics are those which contain the correct cut-out corner size for the maximum volume of the

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