Task: A 10cmx10cm piece of card has equal sized squares removed from each corner. The remainder of card is a net of an open box. Find the maximum volume of the box. Investigate.

Graph to show results using integers with 1 d.p. for the length, height and width

As you can see from the results on the previous page, the largest volume is when the height is at 1.7cm. The next highest is when the height is 1.6 therefore I will continue to investigate between these numbers to 2 decimal places.

As you can see from the results, the largest volume is when the height is at 1.67cm. The next largest is at 1.66 so therefore I will investigate further between the two numbers.

 

As you can see from the results, the highest volume possible (to 3 d.p.) is 74.07407185. This was using a height of 1.667cm.

(10-2X)² x X= V

Task 2: A 9cmx9cm piece of card has equal sized squares removed from each corner. The remainder of card is a net of an open box. Find the maximum volume of the box. Investigate.

As you can see from the previous page, the largest volume is when the height is at 1.5cm. The next largest is at 2 so therefore I will investigate further between the two numbers.

As you can see from the results above, the largest volume is when the height is at 1.5cm. The next largest is at 1.6 so therefore I will investigate further between the two numbers.

As you can see, the numbers are beginning to decrease, so therefore the biggest volume that can be made is 54cm³ using a height of 1.5cm.

(9-2X)² x X= V

Task 3: An 11cmx11cm piece of card has equal sized squares removed from each corner. The remainder of card is a net of an open box. Find the maximum volume of the box. Investigate.

As you can see from the results on the previous page, the largest volume is when the height is 2 with the second largest being 1.5 so therefore I will continue to investigate in between the 2 numbers.

As you can see from the results, the largest volume is when the height is 1.8 with the second highest being 1.9 so therefore I will investigate between the 2 figures.

As you can see from the results on the previous page, the largest volume is made when the height is 1.83 and the second highest is at 1.84 so therefore I will investigate in between the 2 numbers.

As you can see from the results, the biggest volume is made when the height is at 1.833.

(11-2X)² x X= V

I have worked out that the formula for the volume is:

(Box Size-2x height) ² x Height=

Volume

After analyzing my results, I have come to the conclusion that instead of working out the maximum volume by trial and error, it is possible to work out the height by the size of the box e.g.

Box size e.g. 9 divided by 6= 1.5=Height

Height x length x width= Maximum Volume

1.5x6x6=54cm³

(The maximum volume for a 9x9 box)