Math Coursework
The Open Box Problem
An open box is to be made from a sheet of card
Identical squares are to be cut off the four corners of the card as shown in the following diagram
Task:
- For any sized square sheet of card, INVESTIGATE the size of the cut out square, which makes an open box of largest volume
- For any sized rectangular sheet of card, INVESTIGATE the size of the cut out square, which makes an open box of largest volume
In this section of this investigation I am going to investigate using both trial and improvement and spreadsheets which size cutout will give the largest volume of the box. Knowing that this size could go an infinite number of decimal places I have chosen to go to 3 decimal places for the size of the cut out. After investigating the sizes of the cut-outs for 4 different sizes of squares (S2) I will work out the size in a percentage form of the total area of the initial square (S2) using information I have gained from the 4 sizes of squares (S2). After the finding a percentage I will then investigate the sizes for rectangles. I will use 4 different sizes of rectangles for this and will also find the percentage form of the cut out that will get the larges volume for the open box. Finally I will draw a conclusion for both the square card and the rectangular card.
The Square
I will first use a 10 x 10 square
